02_modelFitting_globalTreeModel

Based on code from Martin Holdrege’s Sagebrush-Fire paper

This workflow fits a model across all of CONUS that predicts whether a location does or does not have trees.

The data consists of vegetation % cover by functional group from across CONUS (from AIM, FIA, LANDFIRE, and RAP), as well as climate variables from DayMet, which have been aggregated into mean interannual conditions accross multiple temporal windows.

Dependencies

Set user defined parameters

print(params)

## $run
## [1] FALSE
## 
## $save_figs
## [1] TRUE
## 
## $ecoregion
## [1] "CONUS"
## 
## $response
## [1] "TotalTreeCover"
## 
## $treeThreshold
## [1] 10
## 
## $whichSecondBestMod
## [1] "halfse"
## 
## $thresholdMethod
## [1] "PredPrev=Obs"

# set to true if want to run for a limited number of rows (i.e. for code testing)
test_run <- params$test_run
save_figs <- params$save_figs
response <- params$response
fit_sample <- TRUE # fit model to a sample of the data
n_train <- 5e4 # sample size of the training data
n_test <- 1e6 # sample size of the testing data (if this is too big the decile dotplot code throws memory errors)
run <- params$run
whichSecondBestMod <- params$whichSecondBestMod
treeThreshold <- params$treeThreshold
thresholdMethod <- params$thresholdMethod

Load packages and source functions

# set option so resampled dataset created here reproduces earlier runs of this code with dplyr 1.0.10
source("../../../Functions/glmTransformsIterates.R")
source("../../../Functions/transformPreds.R")
source("../../../Functions/betaLASSO.R")

#source("../../../Functions/StepBeta_mine.R")
#source("src/fig_params.R")
#source("src/modeling_functions.R")
 
library(betareg)
library(ggspatial)
library(terra)
library(tidyterra)
library(sf)
library(caret)
library(tidyverse)
library(GGally) # for ggpairs()
library(pdp) # for partial dependence plots
library(gridExtra)
library(knitr)
library(patchwork) # for figure insets etc. 
library(ggtext)
library(StepBeta)
theme_set(theme_classic())
library(here)
library(rsample)
library(kableExtra)
library(glmnet)
library(USA.state.boundaries)
library(cvms)
library(rsvg)
library(ggimage)
library(doMC)
library(parallel)
library(pROC)

Read in data

Data compiled in the prepDataForModels.R script

here::i_am("Analysis/VegComposition/ModelFitting/02_ModelFitting_globalTreeModel.Rmd")
modDat <- readRDS( here("Data_processed", "CoverData", "DataForModels_spatiallyAveraged_withSoils_noSf_sampledLANDFIRE.rds")) %>% st_drop_geometry()

Prep data

We will fit a binomial model that predicts whether or not there are trees at a location. Because the tree cover data we have is continuous between 0 and 100, we convert it to be binomial be forcing any values ≤ % to be 0, and any values > % to be 1.

modDat <- modDat %>% 
  mutate(TotalTreeCover_binom = replace(TotalTreeCover, TotalTreeCover <=treeThreshold, 0)) %>% 
  mutate(TotalTreeCover_binom = replace(TotalTreeCover_binom, TotalTreeCover_binom > treeThreshold, 1))

set.seed(1234)
# now, rename columns for brevity
modDat_1 <- modDat %>% 
  dplyr::select(-c(prcp_annTotal:annVPD_min)) %>% 
  # mutate(Lon = st_coordinates(.)[,1], 
  #        Lat = st_coordinates(.)[,2])  %>% 
  # st_drop_geometry() %>% 
  # filter(!is.na(newRegion))
  rename("tmin" = tmin_meanAnnAvg_CLIM, 
     "tmax" = tmax_meanAnnAvg_CLIM, #1
     "tmean" = tmean_meanAnnAvg_CLIM, 
     "prcp" = prcp_meanAnnTotal_CLIM, 
     "t_warm" = T_warmestMonth_meanAnnAvg_CLIM,
     "t_cold" = T_coldestMonth_meanAnnAvg_CLIM, 
     "prcp_wet" = precip_wettestMonth_meanAnnAvg_CLIM,
     "prcp_dry" = precip_driestMonth_meanAnnAvg_CLIM, 
     "prcp_seasonality" = precip_Seasonality_meanAnnAvg_CLIM, #2
     "prcpTempCorr" = PrecipTempCorr_meanAnnAvg_CLIM,  #3
     "abvFreezingMonth" = aboveFreezing_month_meanAnnAvg_CLIM, 
     "isothermality" = isothermality_meanAnnAvg_CLIM, #4
     "annWatDef" = annWaterDeficit_meanAnnAvg_CLIM, 
     "annWetDegDays" = annWetDegDays_meanAnnAvg_CLIM,
     "VPD_mean" = annVPD_mean_meanAnnAvg_CLIM, 
     "VPD_max" = annVPD_max_meanAnnAvg_CLIM, #5
     "VPD_min" = annVPD_min_meanAnnAvg_CLIM, #6
     "VPD_max_95" = annVPD_max_95percentile_CLIM, 
     "annWatDef_95" = annWaterDeficit_95percentile_CLIM, 
     "annWetDegDays_5" = annWetDegDays_5percentile_CLIM, 
     "frostFreeDays_5" = durationFrostFreeDays_5percentile_CLIM, 
     "frostFreeDays" = durationFrostFreeDays_meanAnnAvg_CLIM, 
     "soilDepth" = soilDepth, #7
     "clay" = surfaceClay_perc, 
     "sand" = avgSandPerc_acrossDepth, #8
     "coarse" = avgCoarsePerc_acrossDepth, #9
     "carbon" = avgOrganicCarbonPerc_0_3cm, #10
     "AWHC" = totalAvailableWaterHoldingCapacity,
     ## anomaly variables
     tmean_anom = tmean_meanAnnAvg_3yrAnom, #15
     tmin_anom = tmin_meanAnnAvg_3yrAnom, #16
     tmax_anom = tmax_meanAnnAvg_3yrAnom, #17
    prcp_anom = prcp_meanAnnTotal_3yrAnom, #18
      t_warm_anom = T_warmestMonth_meanAnnAvg_3yrAnom,  #19
     t_cold_anom = T_coldestMonth_meanAnnAvg_3yrAnom, #20
      prcp_wet_anom = precip_wettestMonth_meanAnnAvg_3yrAnom, #21
      precp_dry_anom = precip_driestMonth_meanAnnAvg_3yrAnom,  #22
    prcp_seasonality_anom = precip_Seasonality_meanAnnAvg_3yrAnom, #23 
     prcpTempCorr_anom = PrecipTempCorr_meanAnnAvg_3yrAnom, #24
      aboveFreezingMonth_anom = aboveFreezing_month_meanAnnAvg_3yrAnom, #25  
    isothermality_anom = isothermality_meanAnnAvg_3yrAnom, #26
       annWatDef_anom = annWaterDeficit_meanAnnAvg_3yrAnom, #27
     annWetDegDays_anom = annWetDegDays_meanAnnAvg_3yrAnom,  #28
      VPD_mean_anom = annVPD_mean_meanAnnAvg_3yrAnom, #29
      VPD_min_anom = annVPD_min_meanAnnAvg_3yrAnom,  #30
      VPD_max_anom = annVPD_max_meanAnnAvg_3yrAnom,  #31
     VPD_max_95_anom = annVPD_max_95percentile_3yrAnom, #32
      annWatDef_95_anom = annWaterDeficit_95percentile_3yrAnom, #33 
      annWetDegDays_5_anom = annWetDegDays_5percentile_3yrAnom ,  #34
    frostFreeDays_5_anom = durationFrostFreeDays_5percentile_3yrAnom, #35 
      frostFreeDays_anom = durationFrostFreeDays_meanAnnAvg_3yrAnom #36
  ) %>% 
  dplyr::select(-c(tmin_meanAnnAvg_3yr:durationFrostFreeDays_meanAnnAvg_3yr))

Predictors

The following are the candidate predictor variables for this ecoregion:

  prednames <- c(
      "tmean",
      "prcp",
      "prcp_dry", 
      "prcp_seasonality",
      "prcpTempCorr", 
      "isothermality", 
      "annWetDegDays",
      "annWatDef_95", 
      "clay",
      "coarse",
      "AWHC" 
 
 #"tmean", "prcp", "prcp_seasonality", "prcpTempCorr", "isothermality", "annWetDegDays", "sand", "coarse", "AWHC"
  )

print(prednames)

##  [1] "tmean"            "prcp"             "prcp_dry"         "prcp_seasonality"
##  [5] "prcpTempCorr"     "isothermality"    "annWetDegDays"    "annWatDef_95"    
##  [9] "clay"             "coarse"           "AWHC"

Scale the predictor variables for the model-fitting process

allPreds <- modDat_1 %>% 
  dplyr::select(tmin:frostFreeDays,tmean_anom:frostFreeDays_anom, soilDepth:AWHC) %>% 
  names()
modDat_1_s_temp <- modDat_1 %>% 
  mutate(across(all_of(allPreds), base::scale, .names = "{.col}_s")) 
saveRDS(modDat_1_s_temp, file = "./models/scaledModelInputData_yesNoTreeMod.rds")

# Remove the rows that have no observations for total tree cover
modDat_1_s <- modDat_1_s_temp[!is.na(modDat_1_s_temp[,"TotalTreeCover_binom"]),]

# subset the data to only include these predictors, and remove any remaining NAs 
modDat_1_s <- modDat_1_s %>% 
  dplyr::select(prednames, paste0(prednames, "_s"), TotalTreeCover, TotalTreeCover_binom, newRegion, Year, x, y, NA_L1NAME, NA_L2NAME) %>% 
  drop_na()

names(prednames) <- prednames
df_pred <- modDat_1_s[, prednames]

response <- "TotalTreeCover"

Visualize the response variable

ggplot(modDat_1_s) + 
  geom_histogram(aes(TotalTreeCover/100), fill = "forestgreen", col = "forestgreen", alpha = .5) + 
  xlab("Tree Cover") + 
  ggtitle("Untransformed, observed tree cover")

ggplot(modDat_1_s) + 
  geom_histogram(aes(TotalTreeCover_binom), fill = "purple", alpha = .5, col = "purple") +
  xlab("Tree Cover") + 
  ggtitle(paste0("Tree cover, converted to binomial with a ",treeThreshold,"cutoff"))

create_summary <- function(df) {
  df %>% 
    pivot_longer(cols = everything(),
                 names_to = 'variable') %>% 
    group_by(variable) %>% 
    summarise(across(value, .fns = list(mean = ~mean(.x, na.rm = TRUE), min = ~min(.x, na.rm = TRUE), 
                                        median = ~median(.x, na.rm = TRUE), max = ~max(.x, na.rm = TRUE)))) %>% 
    mutate(across(where(is.numeric), round, 4))
}

modDat_1_s[prednames] %>% 
  create_summary() %>% 
  knitr::kable(caption = 'summaries of possible predictor variables') %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed")) 

summaries of possible predictor variables

variable	value_mean	value_min	value_median	value_max
AWHC	14.8606	0.1424	14.2535	35.2881
annWatDef_95	164.3643	0.0000	135.6146	601.2686
annWetDegDays	1854.7754	81.2108	1608.8952	7131.5166
clay	19.7378	0.1687	18.6720	83.0975
coarse	9.3788	0.0000	5.4986	79.9649
isothermality	37.6851	19.4935	37.7091	63.7425
prcp	483.0393	47.6797	399.3619	4360.3490
prcpTempCorr	0.0474	-0.8613	0.1239	0.7098
prcp_dry	3.2466	0.0000	1.6926	81.4306
prcp_seasonality	0.9725	0.3568	0.9379	2.2319
tmean	11.1504	-2.2524	10.0136	24.6330

Histograms of raw and scaled predictors

scaleFigDat_1 <- modDat_1_s %>% 
  dplyr::select(c(x, y, Year, prednames)) %>% 
  pivot_longer(cols = all_of(names(prednames)), 
               names_to = "predNames", 
               values_to = "predValues_unScaled")
scaleFigDat_2 <- modDat_1_s %>% 
  dplyr::select(c(x, y, Year, paste0(prednames, "_s"))) %>% 
  pivot_longer(cols = all_of(paste0(prednames,"_s"
                                    )), 
               names_to = "predNames", 
               values_to = "predValues_scaled", 
               names_sep = ) %>% 
  mutate(predNames = str_replace(predNames, pattern = "_s$", replacement = ""))

scaleFigDat_3 <- scaleFigDat_1 %>% 
  left_join(scaleFigDat_2)

ggplot(scaleFigDat_3) + 
  facet_wrap(~predNames, scales = "free") +
  geom_histogram(aes(predValues_unScaled), fill = "lightgrey", col = "darkgrey") + 
  geom_histogram(aes(predValues_scaled), fill = "lightblue", col = "blue") +
  xlab ("predictor variable values") + 
  ggtitle("Comparing the distribution of unscaled (grey) to scaled (blue) predictor variables")

modDat_1_s <- modDat_1_s %>% 
  rename_with(~paste0(.x, "_raw"), 
                any_of(names(prednames))) %>% 
  rename_with(~str_remove(.x, "_s$"), 
              any_of(paste0(names(prednames), "_s")))

Predictor variables compared to binned response variables

set.seed(12011993)
# vector of name of response variables
vars_response <- response
# longformat dataframes for making boxplots
df_sample_plots <-  modDat_1_s  %>% 
  slice_sample(n = 5e4) %>% 
   rename(response = all_of("TotalTreeCover_binom")) %>% 
  mutate(response = case_when(
    response == 0 ~ "0", 
    response > 0  ~ "1", 
  )) %>% 
  dplyr::select(c(response, prednames)) %>% 
  tidyr::pivot_longer(cols = unname(prednames), 
               names_to = "predictor", 
               values_to = "value"
               )  
 

  ggplot(df_sample_plots, aes_string(x= "response", y = 'value')) +
  geom_boxplot() +
  facet_wrap(~predictor , scales = 'free_y') + 
  ylab("Predictor Variable Values") + 
    xlab(response)

If desired, split the data into training and test data (just leave one year out for now–somewhat randomly chose 2019, 2003, and 2012 )

# # # do a pca of climate across years 
# pca_yrs <- prcomp(modDat_1_s[,paste0(prednames)])
# # library(factoextra)
# (fviz_pca_ind(pca_yrs, habillage = modDat_1_s$Year, label = "none", addEllipses = TRUE, ellipse.level = .95, ggtheme = theme_minimal(), alpha.ind = .1))
# 
# ggplot(modDat_1_s) + 
#   geom_point(aes(modDat_1_s$Year, modDat_1_s$TotalTreeCover)) + 
#   geom_smooth(aes(modDat_1_s$Year, modDat_1_s$TotalTreeCover))

# save test set
modDat_1_sTest <- modDat_1_s[modDat_1_s$Year %in% c(2003, 2012, 2019),]
modDat_1_s <- modDat_1_s[!modDat_1_s$Year %in% c(2003, 2012, 2019),]

Model Fitting

Visualize the spatial blocks and how they differ across environmental space

First, if there are observations in Louisiana, sub-sample them so they’re not so over-represented in the dataset

## make data into spatial format
modDat_1_sf <- modDat_1_s %>% 
  st_as_sf(coords = c("x", "y"), crs = st_crs("EPSG:4326"))


# download map info for visualization
data(state_boundaries_wgs84) 

cropped_states <- suppressMessages(state_boundaries_wgs84 %>%
  dplyr::filter(NAME!="Hawaii") %>%
  dplyr::filter(NAME!="Alaska") %>%
  dplyr::filter(NAME!="Puerto Rico") %>%
  dplyr::filter(NAME!="American Samoa") %>%
  dplyr::filter(NAME!="Guam") %>%
  dplyr::filter(NAME!="Commonwealth of the Northern Mariana Islands") %>%
  dplyr::filter(NAME!="United States Virgin Islands") %>%
  sf::st_sf() %>%
  sf::st_transform(sf::st_crs(modDat_1_sf))) 

## do a pca of climate across level 2 ecoregions
pca <- prcomp(modDat_1_s[,paste0(prednames)])
library(factoextra)
(fviz_pca_ind(pca, habillage = modDat_1_s$NA_L2NAME, label = "none", addEllipses = TRUE, ellipse.level = .95, ggtheme = theme_minimal(), alpha.ind = .1))

# make a table of n for each region
modDat_1_s %>% 
  group_by(NA_L2NAME) %>% 
  dplyr::summarize("Number_Of_Observations" = length(NA_L2NAME)) %>% 
  rename("Level_2_Ecoregion" = NA_L2NAME)%>% 
  kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed")) 

Level_2_Ecoregion	Number_Of_Observations
ATLANTIC HIGHLANDS	827
CENTRAL USA PLAINS	71
COLD DESERTS	144290
EVERGLADES	2
MARINE WEST COAST FOREST	2266
MEDITERRANEAN CALIFORNIA	11356
MISSISSIPPI ALLUVIAL AND SOUTHEAST USA COASTAL PLAINS	1445
MIXED WOOD PLAINS	1179
MIXED WOOD SHIELD	1014
OZARK/OUACHITA-APPALACHIAN FORESTS	1993
SOUTH CENTRAL SEMIARID PRAIRIES	96157
SOUTHEASTERN USA PLAINS	3816
TAMAULIPAS-TEXAS SEMIARID PLAIN	6476
TEMPERATE PRAIRIES	12890
TEXAS-LOUISIANA COASTAL PLAIN	3888
UPPER GILA MOUNTAINS	6949
WARM DESERTS	58351
WEST-CENTRAL SEMIARID PRAIRIES	75472
WESTERN CORDILLERA	35546
WESTERN SIERRA MADRE PIEDMONT	5975

Then, look at the spatial distribution and environmental characteristics of the grouped ecoregions

map1 <- ggplot() +
  geom_sf(data=cropped_states,fill='white') +
  geom_sf(data=modDat_1_sf#[modDat_1_sf$NA_L2NAME %in% c("MIXED WOOD PLAINS"),]
          ,
          aes(fill=as.factor(NA_L2NAME)),linewidth=0.5,alpha=0.5) +
  geom_point(data=modDat_1_s#[modDat_1_s$NA_L2NAME %in% c("MIXED WOOD PLAINS"),]
             ,
             alpha=0.5, 
             aes(x = x, y = y, color=as.factor(NA_L2NAME)), alpha = .1) +
  #scale_fill_okabeito() +
  #scale_color_okabeito() +
 # theme_default() +
  theme(legend.position = 'none') +
  labs(title = "Level 2 Ecoregions as spatial blocks")

hull <- modDat_1_sf %>%
  ungroup() %>%
  group_by(NA_L2NAME) %>%
  slice(chull(tmean, prcp))

plot1<-ggplot(data=modDat_1_sf,aes(x=tmean,y=prcp)) +
  geom_polygon(data = hull, alpha = 0.25,aes(fill=NA_L2NAME) )+
  geom_point(aes(group=NA_L2NAME,color=NA_L2NAME),alpha=0.25) +
  theme_minimal() + xlab("Annual Average T_mean - long-term average") +
  ylab("Annual Average Precip - long-term average") #+
  #scale_color_okabeito() +
  #scale_fill_okabeito()

plot2<-ggplot(data=modDat_1_sf %>%
                pivot_longer(cols=tmean:prcp),
              aes(x=value,group=name)) +
  # geom_polygon(data = hull, alpha = 0.25,aes(fill=fold) )+
  geom_density(aes(group=NA_L2NAME,fill=NA_L2NAME),alpha=0.25) +
  theme_minimal() +
  facet_wrap(~name,scales='free')# +
  #scale_color_okabeito() +
  #scale_fill_okabeito()
 
library(patchwork)
(combo <- (map1+plot1)/plot2) 

# 
# ggplot(data = modDat_1_s) +
#   geom_density(aes(ShrubCover_transformed, col = NA_L2NAME)) +
#   xlim(c(0,100))

Fit a global model with all of the data

First, fit a LASSO regression model using the glmnet R package

• This regression is a beta glm with a logit link (using custom function from Daniel)
• Use cross validation across level 2 ecoregions to tune the lambda parameter in the LASSO model
• this model is fit to using the scaled weather/climate/soils variables
• this list of possible predictors includes:
  1. main effects
  2. interactions between all soils variables
  3. interactions between climate and weather variables
  4. transformed main effects (squared, log-transformed (add a uniform integer – 20– to all variables prior to log-transformation), square root-transformed (add a uniform integer – 20– to all variables prior to log-transformation))

Get rid of transformed predictions and interactions that are correlated

# get first pass of names correlated variables
X_df <- X %>% 
  as.data.frame() %>% 
  dplyr::select(-'(Intercept)')  
corrNames_i <- X_df %>% 
  cor()  %>% 
   caret::findCorrelation(cutoff = .7, verbose = FALSE, names = TRUE, exact = TRUE)
# remove those names that are untransformed main effects 
  # vector of columns to remove 
badNames <- corrNames_i[!(corrNames_i %in% prednames)]
while (sum(!(corrNames_i %in% prednames))>0) {
 corrNames_i <-  X_df %>% 
    dplyr::select(-badNames) %>% 
     cor()  %>% 
   caret::findCorrelation(cutoff = .7, verbose = FALSE, names = TRUE, exact = TRUE)
 # update the vector of names to remove 
 badNames <- unique(c(badNames, corrNames_i[!(corrNames_i %in% prednames)]))
}

## see if there are any correlated variables left (would be all main effects at this point)
# if there are, step through and remove the variable that each is most correlated with 
if (length(corrNames_i)>1) {
  for (i in 1:length(corrNames_i)) {
    X_i <- X_df %>% 
      dplyr::select(-badNames)
    if (corrNames_i[i] %in% names(X_i)) {
    corMat_i <- cor(x = X_i[corrNames_i[i]], y = X_i %>% dplyr::select(-corrNames_i[i])) 
    badNames_i <- colnames(corMat_i)[abs(corMat_i)>=.7]
    # if there are any predictors in the 'badNames_i', remove them from this list
    if (length(badNames_i) > 0 & sum(c(badNames_i %in% prednames))>0) {
        badNames_i <- badNames_i[!(badNames_i %in% prednames)]
    }
    badNames <- unique(c(badNames, badNames_i))
    }
  }
}
## update the X matrix to exclude these correlated variables
X <- X[,!(colnames(X) %in% badNames)]

Run the global LASSO model

if (run == TRUE) {
  # set up custom folds
    # get the ecoregions for training lambda
  train_eco <- modDat_1_s$NA_L2NAME#[train]
  
  # Fit model -----------------------------------------------
  # specify leave-one-year-out cross-validation
  my_folds <- as.numeric(as.factor(train_eco))

    # set up parallel processing
    # this computer has 16 cores (parallel::detectCores())
    registerDoMC(cores = 8)
    
    fit <- cv.glmnet(
      x = X[,2:ncol(X)], 
      y = y, 
      family = "binomial",
      keep = FALSE,
      alpha = 1,  # 0 == ridge regression, 1 == lasso, 0.5 ~~ elastic net
      lambda = lambdas,
      relax = ifelse(response == "ShrubCover", yes = TRUE, no = FALSE),
      #nlambda = 100,
      type.measure="mse",
      #penalty.factor = pen_facts,
      foldid = my_folds,
      #thresh = thresh,
      standardize = FALSE, ## scales variables prior to the model sequence... coefficients are always returned on the original scale
      parallel = TRUE
    )
    base::saveRDS(fit, paste0("../ModelFitting/models/yesOrNoTrees_globalLASSOmod_binomial_treeCutoff_",treeThreshold,".rds"))
    
  
     best_lambda <- fit$lambda.min
  # save the lambda for the most regularized model w/ an MSE that is still 1SE w/in the best lambda model
  lambda_1SE <- fit$lambda.1se
  # save the lambda for the most regularized model w/ an MSE that is still .5SE w/in the best lambda model
  lambda_halfSE <- best_lambda + ((lambda_1SE - best_lambda)/2)
 
## Now, we need to do stability selection to ensure the coefficients that are being chosen with each lambda are stable 

## stability selection for best lambda model 
# setup params
p <- ncol(X[,2:ncol(X)]) # of parameters
n <- length(y) # of observations
n_iter <- 100        # number of subsamples
sample_frac <- 0.75  # fraction of data to subsample
lambda_val <- best_lambda    # fixed lambda value (could be chosen via CV)

# Track selection
selection_counts_bestL <- matrix(0, nrow = p, ncol = 1)

for (i in 1:n_iter) {
  # Subsample rows
  sample_idx <- sample(1:n, size = floor(sample_frac * n), replace = FALSE)
  X_sub <- X[sample_idx, ]
  y_sub <- y[sample_idx]

  # Fit Lasso model
  fit_stab_i <- glmnet(x = X_sub[,2:ncol(X_sub)], y = y_sub, 
    family = "binomial",
    alpha = 1, lambda = lambda_val, standardize = FALSE)

  # Get non-zero coefficients (excluding intercept)
  select_bestL <- which(as.vector(coef(fit_stab_i))[-1] != 0)
  selection_counts_bestL[select_bestL] <- selection_counts_bestL[select_bestL] + 1
}

# Convert counts to selection probabilities (the probability that a variable is selected over 100 iterations)
selection_prob_bestL <- selection_counts_bestL / n_iter
selection_prob_bestL_df <- data.frame(
  VariableNumber = paste0("X", 1:p),
  VariableName = rownames(coef(fit_stab_i))[2:(p+1)],
  SelectionProb = as.vector(selection_prob_bestL)
)

# get those variables that are selected in ≥70% of subsets (Meinshausen and Bühlmann, 2010)
bestLambda_coef <- selection_prob_bestL_df[selection_prob_bestL_df$SelectionProb>=.7, c("VariableName", "SelectionProb")]

#//////
# stability selection for 1se lambda model
lambda_val <-  lambda_1SE    # fixed lambda value (could be chosen via CV)

# Track selection
selection_counts_1seL <- matrix(0, nrow = p, ncol = 1)

for (i in 1:n_iter) {
  # Subsample rows
  sample_idx <- sample(1:n, size = floor(sample_frac * n), replace = FALSE)
  X_sub <- X[sample_idx, ]
  y_sub <- y[sample_idx]

  # Fit Lasso model
  fit_stab_i <- glmnet(x = X_sub[,2:ncol(X_sub)], y = y_sub, 
    family = "binomial",
    alpha = 1, lambda = lambda_val, standardize = FALSE)

  # Get non-zero coefficients (excluding intercept)
  selected_1seL <- which(as.vector(coef(fit_stab_i))[-1] != 0)
  selection_counts_1seL[selected_1seL] <- selection_counts_1seL[selected_1seL] + 1
}

# Convert counts to selection probabilities (the probability that a variable is selected over 100 iterations)
selection_prob_1seL <- selection_counts_1seL / n_iter
selection_prob_1seL_df <- data.frame(
  VariableNumber = paste0("X", 1:p),
  VariableName = rownames(coef(fit_stab_i))[2:(p+1)],
  SelectionProb = as.vector(selection_prob_1seL)
)

# get those variables that are selected in ≥70% of subsets (Meinshausen and Bühlmann, 2010)
seLambda_coef <- selection_prob_1seL_df[selection_prob_1seL_df$SelectionProb>=.7, c("VariableName", "SelectionProb")]

# stability selection for half se lambda model
lambda_val <- lambda_halfSE    # fixed lambda value (could be chosen via CV)

# Track selection
selection_counts_halfseL <- matrix(0, nrow = p, ncol = 1)

for (i in 1:n_iter) {
  # Subsample rows
  sample_idx <- sample(1:n, size = floor(sample_frac * n), replace = FALSE)
  X_sub <- X[sample_idx, ]
  y_sub <- y[sample_idx]

  # Fit Lasso model
  fit_stab_i <- glmnet(x = X_sub[,2:ncol(X_sub)], y = y_sub, 
    family = "binomial",
    alpha = 1, lambda = lambda_val, standardize = FALSE)

  # Get non-zero coefficients (excluding intercept)
  selected_halfseL <- which(as.vector(coef(fit_stab_i))[-1] != 0)
  selection_counts_halfseL[selected_halfseL] <- selection_counts_halfseL[selected_halfseL] + 1
}

# Convert counts to selection probabilities (the probability that a variable is selected_halfseL over 100 iterations)
selection_prob_halfseL <- selection_counts_halfseL / n_iter
selection_prob_halfseL_df <- data.frame(
  VariableNumber = paste0("X", 1:p),
  VariableName = rownames(coef(fit_stab_i))[2:(p+1)],
  SelectionProb = as.vector(selection_prob_halfseL)
)

# get those variables that are selected_halfseL_halfseL in ≥70% of subsets (Meinshausen and Bühlmann, 2010)
halfseLambda_coef <- selection_prob_halfseL_df[selection_prob_halfseL_df$SelectionProb>=.7, c("VariableName", "SelectionProb")]

## fit w/ the identified coefficients from the 'best' lambda, but using the glm function
  mat_glmnet_best <- bestLambda_coef$VariableName 

  if (length(mat_glmnet_best) == 0) {
    f_glm_bestLambda <- as.formula(paste0("TotalTreeCover_binom", "~ 1"))
  } else {
  f_glm_bestLambda <- as.formula(paste0("TotalTreeCover_binom", " ~ ", paste0(mat_glmnet_best, collapse = " + ")))
  }
  
## fit using betareg
  fit_glm_bestLambda <- fit_glm_bestLambda_binomial <- glm(formula = f_glm_bestLambda, data = modDat_1_s, family = binomial)
    
   ## fit w/ the identified coefficients from the '1se' lambda, but using the glm function
  mat_glmnet_1se <- seLambda_coef$VariableName
    
  if (length(mat_glmnet_1se) == 0) {
    f_glm_1se <- as.formula(paste0("TotalTreeCover_binom", "~ 1"))
  } else {
  f_glm_1se <- as.formula(paste0("TotalTreeCover_binom", " ~ ", paste0(mat_glmnet_1se, collapse = " + ")))
  }


  fit_glm_se <- glm(formula = f_glm_1se, data = modDat_1_s, family = binomial)
  # glm(data = modDat_1_s, formula = f_glm_1se,
  #                   family =  stats::Gamma(link = "log"))
  
     ## fit w/ the identified coefficients from the '.5se' lambda, but using the glm function
  mat_glmnet_halfse <- halfseLambda_coef$VariableName
  
  if (length(mat_glmnet_halfse) == 0) {
    f_glm_halfse <- as.formula(paste0("TotalTreeCover_binom", "~ 1"))
  } else {
  f_glm_halfse <- as.formula(paste0("TotalTreeCover_binom", " ~ ", paste0(mat_glmnet_halfse, collapse = " + ")))
  }

  fit_glm_halfse <- glm(formula = f_glm_halfse, data = modDat_1_s, family = binomial )
  
  ## save models 
  saveRDS(fit_glm_bestLambda, paste0("./models/yesOrNoTrees_bestLambdaGLM_",treeThreshold,".rds"))
  saveRDS(fit_glm_halfse, paste0("./models/yesOrNoTrees_halfSELambdaGLM_",treeThreshold,".rds"))
  saveRDS(fit_glm_se, paste0("./models/yesOrNoTrees_oneSELambdaGLM_",treeThreshold,".rds"))
    
  ## save the R environment after running the models 
  save(f_glm_halfse, mat_glmnet_halfse, halfseLambda_coef,
              f_glm_1se, mat_glmnet_1se, seLambda_coef,
              f_glm_bestLambda, mat_glmnet_best, bestLambda_coef,
              file = paste0("./models/interimModelFittingObjects_yesOrNoTrees_binomial_",treeThreshold,".rds"))
  } else {
    # read in LASSO object
    fit <- readRDS(paste0("../ModelFitting/models/yesOrNoTrees_globalLASSOmod_binomial_treeCutoff_",treeThreshold,".rds"))
    
    # read in R objects having to do w/ model fitting 
    load(file = paste0("./models/interimModelFittingObjects_yesOrNoTrees_binomial_",treeThreshold,".rds"))
      
  fit_glm_bestLambda <- readRDS(paste0("./models/yesOrNoTrees_bestLambdaGLM_",treeThreshold,".rds"))
  fit_glm_halfse <- readRDS(paste0("./models/yesOrNoTrees_halfSELambdaGLM_",treeThreshold,".rds"))
  fit_glm_se <- readRDS(paste0("./models/yesOrNoTrees_oneSELambdaGLM_",treeThreshold,".rds"))
  }


  # assess model fit
  # assess.glmnet(fit$fit.preval, #newx = X[,2:293], 
  #               newy = y, family = stats::Gamma(link = "log"))
  # save the minimum lambda
  best_lambda <- fit$lambda.min
  # save the lambda for the most regularized model w/ an MSE that is still 1SE w/in the best lambda model
  lambda_1SE <- fit$lambda.1se
  # save the lambda for the most regularized model w/ an MSE that is still .5SE w/in the best lambda model
  lambda_halfSE <- best_lambda + ((lambda_1SE - best_lambda)/2)
 
  print(fit)     

## 
## Call:  cv.glmnet(x = X[, 2:ncol(X)], y = y, lambda = lambdas, type.measure = "mse",      foldid = my_folds, keep = FALSE, parallel = TRUE, relax = ifelse(response ==          "ShrubCover", yes = TRUE, no = FALSE), family = "binomial",      alpha = 1, standardize = FALSE) 
## 
## Measure: Mean-Squared Error 
## 
##      Lambda Index Measure      SE Nonzero
## min 0.00365   115  0.2447 0.03089      22
## 1se 0.04150    80  0.2736 0.02847       5

  plot(fit)

Then, we predict (on the training set) using both of these models (best lambda and 1se lambda) as an itial test

  ## predict on the test data
  # lasso model predictions with the optimal lambda
  optimal_pred <- stats::predict(fit_glm_bestLambda, #newx=X[,2:ncol(X)], 
                                 type = "response")
  optimal_pred_1se <-  stats::predict(fit_glm_se, newx=X[,2:ncol(X)], type = "response")
  optimal_pred_halfse <- stats::predict(fit_glm_halfse, newx = X[,2:ncol(X)], type = "response")
  
    null_fit <- glm(
      formula = y ~ 1, #data = modDat_1_s, 
      family = binomial
      )
  null_pred <- predict(null_fit, newdata = as.data.frame(X), type = "response"
                       )

  # save data
  fullModOut <- list(
    "modelObject" = fit,
    "nullModelObject" = null_fit,
    "modelPredictions" = data.frame(#ecoRegion_holdout = rep(test_eco,length(y)),
      obs=y,
                    pred_opt=optimal_pred, 
                    pred_opt_se = optimal_pred_1se,
                    pred_opt_halfse = optimal_pred_halfse,
                    pred_null=null_pred#,
                    #pred_nopenalty=nopen_pred
                    ))

ggplot() + 
  geom_point(aes(X[,2], fullModOut$modelPredictions$obs), col = "black", alpha = .1) + 
  geom_point(aes(X[,2], fullModOut$modelPredictions$pred_opt), col = "red", alpha = .1) + ## predictions w/ the CV model (best lambda)
  geom_point(aes(X[,2], fullModOut$modelPredictions$pred_opt_halfse), col = "orange", alpha = .1) + ## predictions w/ the CV model (.5se lambda)
  geom_point(aes(X[,2], fullModOut$modelPredictions$pred_opt_se), col = "green", alpha = .1) + ## predictions w/ the CV model (1se lambda)
  geom_point(aes(X[,2], fullModOut$modelPredictions$pred_null), col = "blue", alpha = .1) + 
  labs(title = "A rough comparison of observed and model-predicted values", 
       subtitle = "black = observed values \n red = predictions from 'best lambda' model \n orange = predictions for '1/2se' lambda model \n green = predictions from '1se' lambda model \n blue = predictions from null model") +
  xlab(colnames(X)[2])

  #ylim(c(0,200))

The internal cross-validation process to fit the global LASSO model identified an optimal lambda value (regularization parameter) of r{print(best_lambda)}. The lambda value such that the cross validation error is within 1 standard error of the minimum (“1se lambda”) was `r{print(fit$lambda.1se)}`` . The following coefficients were kept in each model:

# the coefficient matrix from the 'best model' -- find and print those coefficients that aren't 0 in a table
coef_glm_bestLambda <- coef(fit_glm_bestLambda) %>% 
  data.frame() 
coef_glm_bestLambda$coefficientName <- rownames(coef_glm_bestLambda)
names(coef_glm_bestLambda)[1] <- "coefficientValue_bestLambda"
# coefficient matrix from the '1se' model 
coef_glm_1se <- coef(fit_glm_se) %>% 
  data.frame() 
coef_glm_1se$coefficientName <- rownames(coef_glm_1se)
names(coef_glm_1se)[1] <- "coefficientValue_1seLambda"
# coefficient matrix from the 'half se' model 
coef_glm_halfse <- coef(fit_glm_halfse) %>% 
  data.frame() 
coef_glm_halfse$coefficientName <- rownames(coef_glm_halfse)
names(coef_glm_halfse)[1] <- "coefficientValue_halfseLambda"
# add together
coefs <- full_join(coef_glm_bestLambda, coef_glm_halfse) %>% 
  full_join(coef_glm_1se) %>% 
  dplyr::select(coefficientName, coefficientValue_bestLambda,
                coefficientValue_halfseLambda, coefficientValue_1seLambda)

globModTerms <- coefs[!is.na(coefs$coefficientValue_bestLambda), "coefficientName"]

## also, get the number of unique variables in each model 
var_prop_pred <- paste0(response, "_pred")
response_vars <- c(response, var_prop_pred)
# for best lambda model
prednames_fig <- paste(str_split(globModTerms, ":", simplify = TRUE)) 
prednames_fig <- str_replace(prednames_fig, "I\\(", "")
prednames_fig <- str_replace(prednames_fig, "\\^2\\)", "")
prednames_fig <- unique(prednames_fig[prednames_fig>0])
prednames_fig <- prednames_fig
prednames_fig_num <- length(prednames_fig)
# for 1SE lambda model
globModTerms_1se <- coefs[!is.na(coefs$coefficientValue_1seLambda), "coefficientName"]
if (length(globModTerms_1se) == 1) {
prednames_fig_1se <- paste(str_split(globModTerms_1se, ":", simplify = TRUE)) 
prednames_fig_1se <- str_replace(prednames_fig_1se, "I\\(", "")
prednames_fig_1se <- str_replace(prednames_fig_1se, "\\^2\\)", "")
prednames_fig_1se <- unique(prednames_fig_1se[prednames_fig_1se>0])
prednames_fig_1se_num <- c(0)
} else {
prednames_fig_1se <- paste(str_split(globModTerms_1se, ":", simplify = TRUE)) 
prednames_fig_1se <- str_replace(prednames_fig_1se, "I\\(", "")
prednames_fig_1se <- str_replace(prednames_fig_1se, "\\^2\\)", "")
prednames_fig_1se <- unique(prednames_fig_1se[prednames_fig_1se>0])
prednames_fig_1se_num <- length(prednames_fig_1se)
}
# for 1/2SE lambda model
globModTerms_halfse <- coefs[!is.na(coefs$coefficientValue_halfseLambda), "coefficientName"]
if (length(globModTerms_halfse) == 1) {
prednames_fig_halfse <- paste(str_split(globModTerms_halfse, ":", simplify = TRUE)) 
prednames_fig_halfse <- str_replace(prednames_fig_halfse, "I\\(", "")
prednames_fig_halfse <- str_replace(prednames_fig_halfse, "\\^2\\)", "")
prednames_fig_halfse <- unique(prednames_fig_halfse[prednames_fig_halfse>0])
prednames_fig_halfse_num <- c(0)
} else {
prednames_fig_halfse <- paste(str_split(globModTerms_halfse, ":", simplify = TRUE)) 
prednames_fig_halfse <- str_replace(prednames_fig_halfse, "I\\(", "")
prednames_fig_halfse <- str_replace(prednames_fig_halfse, "\\^2\\)", "")
prednames_fig_halfse <- unique(prednames_fig_halfse[prednames_fig_halfse>0])
prednames_fig_halfse_num <- length(prednames_fig_halfse)
}
# make a table
kable(coefs, col.names = c("Coefficient Name", "Value from best lambda model", 
                           "Value from 1/2 se lambda", "Value from 1se lambda model")
      ) %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed")) 

Coefficient Name	Value from best lambda model	Value from 1/2 se lambda	Value from 1se lambda model
(Intercept)	-0.6747817	-0.8616112	-1.3908996
prcp	1.7134506	1.9694935	1.8591155
prcp_seasonality	-0.0163393	-0.3086721	-0.5178721
prcpTempCorr	-0.9128524	-0.5967287	-0.2352708
annWetDegDays	0.5337744	NA	NA
annWatDef_95	-0.6052394	NA	NA
coarse	0.2057888	NA	NA
AWHC	-0.6156823	-0.7655963	-0.8858988
I(tmean^2)	-0.3181863	NA	NA
I(prcp_seasonality^2)	0.2010413	NA	NA
I(prcpTempCorr^2)	-0.8905565	-0.6416890	NA
I(isothermality^2)	0.1422692	NA	NA
I(clay^2)	-0.1181021	-0.1661580	-0.1421531
I(AWHC^2)	0.1127803	NA	NA
annWetDegDays:annWatDef_95	0.9165646	NA	NA
prcp_dry:isothermality	-0.2965084	-0.4376182	NA
prcpTempCorr:isothermality	-0.0206105	NA	NA
isothermality:tmean	-0.2850425	NA	NA
prcpTempCorr:prcp_dry	0.5054909	NA	NA
prcpTempCorr:tmean	-0.2528563	NA	NA
AWHC:clay	-0.1629028	-0.2506869	NA
coarse:clay	0.0916325	NA	NA

# calculate RMSE of all models 
RMSE_best <- yardstick::rmse(fullModOut$modelPredictions[,c("obs", "pred_opt")], truth = "obs", estimate = "pred_opt")$.estimate
RMSE_halfse <- yardstick::rmse(fullModOut$modelPredictions[,c("obs", "pred_opt_halfse")], truth = "obs", estimate = "pred_opt_halfse")$.estimate
RMSE_1se <- yardstick::rmse(fullModOut$modelPredictions[,c("obs", "pred_opt_se")], truth = "obs", estimate = "pred_opt_se")$.estimate
# calculate bias of all models
bias_best <-  mean((fullModOut$modelPredictions$obs) - fullModOut$modelPredictions$pred_opt)
bias_halfse <-  mean((fullModOut$modelPredictions$obs) - fullModOut$modelPredictions$pred_opt_halfse)
bias_1se <- mean((fullModOut$modelPredictions$obs) - fullModOut$modelPredictions$pred_opt_se)

uniqueCoeffs <- data.frame("Best lambda model" = c(signif(RMSE_best,3), as.character(signif(bias_best, 3)),
  as.integer(length(globModTerms)-1), as.integer(prednames_fig_num), 
                                                   as.integer(sum(prednames_fig %in% c(prednames_clim))),
                                                   as.integer(sum(prednames_fig %in% c(prednames_weath))),
                                                   as.integer(sum(prednames_fig %in% c(prednames_soils)))
                                                   ), 
                           "1/2 se lambda model" = c(signif(RMSE_halfse,3), as.character(signif(bias_halfse, 3)),
                             length(globModTerms_halfse)-1, prednames_fig_halfse_num,
                                                   sum(prednames_fig_halfse %in% c(prednames_clim)),
                                                   sum(prednames_fig_halfse %in% c(prednames_weath)),
                                                   sum(prednames_fig_halfse %in% c(prednames_soils))), 
                           "1se lambda model" = c(signif(RMSE_1se,3), as.character(signif(bias_1se, 3)),
                             length(globModTerms_1se)-1, prednames_fig_1se_num,
                                                   sum(prednames_fig_1se %in% c(prednames_clim)),
                                                   sum(prednames_fig_1se %in% c(prednames_weath)),
                                                   sum(prednames_fig_1se %in% c(prednames_soils))))
row.names(uniqueCoeffs) <- c("RMSE", "bias: mean(obs-pred.)", "Total number of coefficients", "Number of unique coefficients",
                             "Number of unique climate coefficients", 
                             "Number of unique weather coefficients",  
                             "Number of unique soils coefficients"
                             )

kable(uniqueCoeffs, 
      col.names = c("Best lambda model", "1/2 se lambda model", "1se lambda model"), row.names = TRUE) %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed")) 

	Best lambda model	1/2 se lambda model	1se lambda model
RMSE	0.315	0.323	0.333
bias: mean(obs-pred.)	-2.79e-14	-2.15e-13	8.62e-14
Total number of coefficients	21	8	5
Number of unique coefficients	11	7	5
Number of unique climate coefficients	8	5	3
Number of unique weather coefficients	0	0	0
Number of unique soils coefficients	3	2	2

Visualizations of Model Predictions and Residuals

In the following figures, we show model predictions made using the best lambda model, as well as an alternative “second-best” lambda model. As the alternative to the best lambda model, we use the model (1se or 1/2se of best Lambda) that has the fewest number of unique predictors, but is not a null model.

if (whichSecondBestMod == "auto") {
  # name of model w/ fewest # of predictors (but more than 0)
uniqueCoeff_min <- min(as.numeric(uniqueCoeffs[4,2:3])[which(as.numeric(uniqueCoeffs[4,2:3]) > 0)])
alternativeModel <- names(uniqueCoeffs[4,2:3])[which(uniqueCoeffs[4,2:3] == uniqueCoeff_min)]

if (is.finite(uniqueCoeff_min)) {
  if (length(alternativeModel) == 1) {
  if (alternativeModel == "X1.2.se.lambda.model") {
  mod_secondBest <- fit_glm_halfse
  name_secondBestMod <- "1/2 SE Model"
  prednames_secondBestMod <- prednames_fig_halfse
  # get the name of the column that contains the prediction data for only the training data, for this model
trainDatPredName <- "pred_opt_halfse"
} else if (alternativeModel == "X1se.lambda.model") {
  mod_secondBest <- fit_glm_se
  name_secondBestMod <- "1 SE Model"
  prednames_secondBestMod <- prednames_fig_1se
  # get the name of the column that contains the prediction data for only the training data, for this model
trainDatPredName <- "pred_opt_se"
}
} else {
  # if both alternative models have the same number of unique coefficients, chose the model that has the fewest number of total predictors
  uniqueCoeff_min2 <- min(as.numeric(uniqueCoeffs[3,alternativeModel]))
alternativeModel2 <- names(uniqueCoeffs[3,alternativeModel])[which(uniqueCoeffs[3,alternativeModel] == uniqueCoeff_min2)]
if (length(alternativeModel2) == 1) {
  if (alternativeModel2 == "X1.2.se.lambda.model") {
  mod_secondBest <- fit_glm_halfse
  name_secondBestMod <- "1/2 SE Model"
  prednames_secondBestMod <- prednames_fig_halfse
   # get the name of the column that contains the prediction data for only the training data, for this model
trainDatPredName <- "pred_opt_halfse"
} else if (alternativeModel2 == "X1se.lambda.model") {
  mod_secondBest <- fit_glm_se
  name_secondBestMod <- "1 SE Model"
  prednames_secondBestMod <- prednames_fig_1se
  # get the name of the column that contains the prediction data for only the training data, for this model
trainDatPredName <- "pred_opt_se"
}
} else {
  mod_secondBest <- fit_glm_halfse
  name_secondBestMod <- "1/2 SE Model"
  prednames_secondBestMod <- prednames_fig_halfse
  # get the name of the column that contains the prediction data for only the training data, for this model
trainDatPredName <- "pred_opt_halfse"
}

}
  }else {
    mod_secondBest <- NULL
  name_secondBestMod <- "Intercept_Only"
  prednames_secondBestMod <- NULL
}
} else if (whichSecondBestMod == "1se") {
  mod_secondBest <- fit_glm_se
  name_secondBestMod <- "1 SE Model"
  prednames_secondBestMod <- prednames_fig_1se
# get the name of the column that contains the prediction data for only the training data, for this model
trainDatPredName <- "pred_opt_se"
} else if (whichSecondBestMod == "halfse") {
  mod_secondBest <- fit_glm_halfse
  name_secondBestMod <- "1/2 SE Model"
  prednames_secondBestMod <- prednames_fig_halfse
  # get the name of the column that contains the prediction data for only the training data, for this model
trainDatPredName <- "pred_opt_halfse"
}

Predict on the test data and then the complete dataset

  # create prediction for each each model
# (i.e. for each fire proporation variable)
predict_by_response <- function(mod, df) {
  df_out <- df
  response_name <- paste0("TotalTreeCover_binom", "_pred")
  preds <- predict(mod, newdata = df_out, #s="lambda.min", 
                                     type = "response")
  #preds[preds<0] <- 0
  #preds[preds>100] <- 100
  df_out <- df_out %>% cbind(preds)
   colnames(df_out)[ncol(df_out)] <- response_name
  return(df_out)
}
## predict on the test dataset
pred_glm1_test <- predict_by_response(fit_glm_bestLambda, modDat_1_sTest)#X[,2:ncol(X)])
pred_glm1_test$resid <- pred_glm1_test[,"TotalTreeCover_binom"] - pred_glm1_test[,paste0("TotalTreeCover_binom", "_pred")]
pred_glm1_test$extremeResid <- NA
pred_glm1_test[pred_glm1_test$resid > .5 | pred_glm1_test$resid < -.5,"extremeResid"] <- 1

## predict on entire dataset
pred_glm1_full <- predict_by_response(fit_glm_bestLambda, rbind(modDat_1_sTest, modDat_1_s))#X[,2:ncol(X)])
pred_glm1_full$resid <- pred_glm1_full[,"TotalTreeCover_binom"] - pred_glm1_full[,paste0("TotalTreeCover_binom", "_pred")]
pred_glm1_full$extremeResid <- NA
pred_glm1_full[pred_glm1_full$resid > .5 | pred_glm1_full$resid < -.5,"extremeResid"] <- 1

if ( name_secondBestMod == "Intercept_Only") {
  print("The next best lambda model only contains one predictor (an intercept)")
} else {

pred_glm1_1se_test <- predict_by_response(mod_secondBest, modDat_1_sTest)#X[,2:ncol(X)])
pred_glm1_1se_test$resid <- pred_glm1_1se_test[,"TotalTreeCover_binom"] - pred_glm1_1se_test[,paste0("TotalTreeCover_binom", "_pred")]
pred_glm1_1se_test$extremeResid <- NA
pred_glm1_1se_test[pred_glm1_1se_test$resid > .5 | pred_glm1_1se_test$resid < -.5,"extremeResid"] <- 1

## for full dataset
pred_glm1_1se_full <- predict_by_response(mod_secondBest, rbind(modDat_1_sTest, modDat_1_s))#X[,2:ncol(X)])
pred_glm1_1se_full$resid <- pred_glm1_1se_full[,"TotalTreeCover_binom"] - pred_glm1_1se_full[,paste0("TotalTreeCover_binom", "_pred")]
pred_glm1_1se_full$extremeResid <- NA
pred_glm1_1se_full[pred_glm1_1se_full$resid > .5 | pred_glm1_1se_full$resid < -.5,"extremeResid"] <- 1
}

Inital Model Diagnostics

Identifying the optimal threshold based on the prevalence in the training data. ROC Curves based on classification accuracy of the model when used on the testing set (held-out years 2003, 2012 and 2019)

For the bestLambda model:

library(PresenceAbsence)
DATA <- fullModOut$modelPredictions[,c("obs", "pred_opt")] # only training data
DATA$ID <- 1:nrow(DATA)
#pred.prev <- predicted.prevalence(DATA = DATA[,c("ID", "TotalTreeCover_binom", "TotalTreeCover_binom_pred")], threshold = 20)
#accu <- presence.absence.accuracy(DATA[,c("ID", "TotalTreeCover_binom", "TotalTreeCover_binom_pred")], threshold = 20)
optimalThresholds <- optimal.thresholds(DATA = DATA[,c("ID", "obs", "pred_opt")], 
                                        threshold = 200, obs.prev = mean(DATA[,"obs"])) # tests 100 thresholds)
rm(DATA)
best_threshold_bestLambda <- optimalThresholds[optimalThresholds$Method == thresholdMethod, 2]
cat(paste0("Optimal threshold for best lambda model based on ROC curve, based on the ",thresholdMethod, " method: ", best_threshold_bestLambda, "\n"))

## Optimal threshold for best lambda model based on ROC curve, based on the PredPrev=Obs method: 0.381909547738693

# Now make an ROC curve based on the test set
roc_curve <- roc(pred_glm1_test$TotalTreeCover_binom, pred_glm1_test$TotalTreeCover_binom_pred)
# Plot ROC curve
plot(roc_curve, main =  paste0("ROC Curve for best lambda model \n","AUC: ",round(roc_curve$auc,2)))

For the second-bestLambda model:

# best_threshold_secondBest <- coords$threshold
DATA <- fullModOut$modelPredictions[,c("obs", trainDatPredName)]
DATA$ID <- 1:nrow(DATA)
#pred.prev <- predicted.prevalence(DATA = DATA[,c("ID", "TotalTreeCover_binom", "TotalTreeCover_binom_pred")], threshold = 20)
#accu <- presence.absence.accuracy(DATA[,c("ID", "TotalTreeCover_binom", "TotalTreeCover_binom_pred")], threshold = 20)
optimalThresholds <- optimal.thresholds(DATA = DATA[,c("ID", "obs", trainDatPredName)], 
                                        threshold = 200, obs.prev = mean(DATA[,"obs"])) # tests 100 thresholds)
rm(DATA)
best_threshold_secondBest <- optimalThresholds[optimalThresholds$Method == thresholdMethod, 2]
cat(paste0("Optimal threshold for second-best lambda model based on ROC curve, based on the ",thresholdMethod, " method: ", best_threshold_secondBest, "\n"))

## Optimal threshold for second-best lambda model based on ROC curve, based on the PredPrev=Obs method: 0.346733668341709

# Now make an ROC curve based on the test set
roc_curve_secondBest <- roc(pred_glm1_1se_test$TotalTreeCover_binom, pred_glm1_1se_test$TotalTreeCover_binom_pred, smooth = FALSE)
# Plot ROC curve
plot(roc_curve_secondBest, main =  paste0("ROC Curve for second-best lambda model \n","AUC: ",round(roc_curve_secondBest$auc,2)))

Use the identified thresholds to make predictions binary

## for test dataset
# best lambda model
# "binomialize" the continuous predictions
pred_glm1_test <- pred_glm1_test %>% 
  mutate(TotalTreeCover_binom_pred_binary = TotalTreeCover_binom_pred,
    TotalTreeCover_binom_pred_binary = replace(TotalTreeCover_binom_pred_binary, TotalTreeCover_binom_pred_binary > best_threshold_bestLambda, 1),
         TotalTreeCover_binom_pred_binary = replace(TotalTreeCover_binom_pred_binary, TotalTreeCover_binom_pred_binary <= best_threshold_bestLambda, 0)) 

# second-best lambda model
# "binomialize" the continuouse predictions
pred_glm1_1se_test <- pred_glm1_1se_test %>% 
  mutate(TotalTreeCover_binom_pred_binary = TotalTreeCover_binom_pred,
    TotalTreeCover_binom_pred_binary = replace(TotalTreeCover_binom_pred_binary, TotalTreeCover_binom_pred_binary > best_threshold_secondBest, 1),
         TotalTreeCover_binom_pred_binary = replace(TotalTreeCover_binom_pred_binary, TotalTreeCover_binom_pred_binary <= best_threshold_secondBest, 0)) 

## for full dataset
# best lambda model
# "binomialize" the continuous predictions
pred_glm1_full <- pred_glm1_full %>% 
  mutate(TotalTreeCover_binom_pred_binary = TotalTreeCover_binom_pred,
    TotalTreeCover_binom_pred_binary = replace(TotalTreeCover_binom_pred_binary, TotalTreeCover_binom_pred_binary > best_threshold_bestLambda, 1),
         TotalTreeCover_binom_pred_binary = replace(TotalTreeCover_binom_pred_binary, TotalTreeCover_binom_pred_binary <= best_threshold_bestLambda, 0)) 

# second-best lambda model
# "binomialize" the continuouse predictions
pred_glm1_1se_full <- pred_glm1_1se_full %>% 
  mutate(TotalTreeCover_binom_pred_binary = TotalTreeCover_binom_pred,
    TotalTreeCover_binom_pred_binary = replace(TotalTreeCover_binom_pred_binary, TotalTreeCover_binom_pred_binary > best_threshold_secondBest, 1),
         TotalTreeCover_binom_pred_binary = replace(TotalTreeCover_binom_pred_binary, TotalTreeCover_binom_pred_binary <= best_threshold_secondBest, 0)) 

Identify Misclassifications

# true positive = tree (1)
# false positive = model says tree, data says no-tree (2) 
# true negative = no tree (3) 
# false negative = model says no tree, data says tree (4)

# best lambda model - test dataset
pred_glm1_test$missClass <- NA
pred_glm1_test[pred_glm1_test$TotalTreeCover_binom == 1 & 
                 pred_glm1_test$TotalTreeCover_binom_pred_binary == 1, "missClass"] <- 1
pred_glm1_test[pred_glm1_test$TotalTreeCover_binom == 0 & 
                 pred_glm1_test$TotalTreeCover_binom_pred_binary == 0, "missClass"] <- 3
pred_glm1_test[pred_glm1_test$TotalTreeCover_binom == 0 & 
                 pred_glm1_test$TotalTreeCover_binom_pred_binary == 1, "missClass"] <- 2
pred_glm1_test[pred_glm1_test$TotalTreeCover_binom == 1 & 
                 pred_glm1_test$TotalTreeCover_binom_pred_binary == 0, "missClass"] <- 4

# best lambda model - full dataset
pred_glm1_full$missClass <- NA
pred_glm1_full[pred_glm1_full$TotalTreeCover_binom == 1 & 
                 pred_glm1_full$TotalTreeCover_binom_pred_binary == 1, "missClass"] <- 1
pred_glm1_full[pred_glm1_full$TotalTreeCover_binom == 0 & 
                 pred_glm1_full$TotalTreeCover_binom_pred_binary == 0, "missClass"] <- 3
pred_glm1_full[pred_glm1_full$TotalTreeCover_binom == 0 & 
                 pred_glm1_full$TotalTreeCover_binom_pred_binary == 1, "missClass"] <- 2
pred_glm1_full[pred_glm1_full$TotalTreeCover_binom == 1 & 
                 pred_glm1_full$TotalTreeCover_binom_pred_binary == 0, "missClass"] <- 4

# second-best lambda model - test dataset
pred_glm1_1se_test$missClass <- NA
pred_glm1_1se_test[pred_glm1_1se_test$TotalTreeCover_binom == 1 & 
                 pred_glm1_1se_test$TotalTreeCover_binom_pred_binary == 1, "missClass"] <- 1
pred_glm1_1se_test[pred_glm1_1se_test$TotalTreeCover_binom == 0 & 
                 pred_glm1_1se_test$TotalTreeCover_binom_pred_binary == 0, "missClass"] <- 3
pred_glm1_1se_test[pred_glm1_1se_test$TotalTreeCover_binom == 0 & 
                 pred_glm1_1se_test$TotalTreeCover_binom_pred_binary == 1, "missClass"] <- 2
pred_glm1_1se_test[pred_glm1_1se_test$TotalTreeCover_binom == 1 & 
                 pred_glm1_1se_test$TotalTreeCover_binom_pred_binary == 0, "missClass"] <- 4

# second-best lambda model - full dataset
pred_glm1_1se_full$missClass <- NA
pred_glm1_1se_full[pred_glm1_1se_full$TotalTreeCover_binom == 1 & 
                 pred_glm1_1se_full$TotalTreeCover_binom_pred_binary == 1, "missClass"] <- 1
pred_glm1_1se_full[pred_glm1_1se_full$TotalTreeCover_binom == 0 & 
                 pred_glm1_1se_full$TotalTreeCover_binom_pred_binary == 0, "missClass"] <- 3
pred_glm1_1se_full[pred_glm1_1se_full$TotalTreeCover_binom == 0 & 
                 pred_glm1_1se_full$TotalTreeCover_binom_pred_binary == 1, "missClass"] <- 2
pred_glm1_1se_full[pred_glm1_1se_full$TotalTreeCover_binom == 1 & 
                 pred_glm1_1se_full$TotalTreeCover_binom_pred_binary == 0, "missClass"] <- 4

Maps of Observations, Predictions, and Residuals

Observations - continuous and binary total tree cover for the full dataset

# rasterize
# get reference raster
# use the gridMet raster 
test_rast_dayMet <- rast("../../../Data_raw/dayMet/rawMonthlyData/orders/70e0da02b9d2d6e8faa8c97d211f3546/Daymet_Monthly_V4R1/data/daymet_v4_prcp_monttl_na_1980.tif") %>%
  #terra::project(terra::crs("EPSG:4326")) %>%
  terra::crop(ext(-2000000, 2600000, -1900000, 1500000))

## aggregate to a 4x4km^2 grid
test_rast <- test_rast_dayMet %>% 
  terra::aggregate(fact = 8, fun = "mean")
# test_rast_Untranfsormed <-  rast("../../../Data_raw/gridMet/pr_2020.nc") #%>% ## mean cell size of unaggregated grid size (16709380m^2)
# test_rast <- test_rast_Untranfsormed %>% 
#    terra::aggregate(fact = 2, fun = "mean") #%>% 
regions <- sf::st_read(dsn = "../../../Data_raw/Level2Ecoregions/", layer = "NA_CEC_Eco_Level2") 

## Reading layer `NA_CEC_Eco_Level2' from data source 
##   `/Users/astears/Documents/Dropbox_static/Work/NAU_USGS_postdoc/cleanPED/PED_vegClimModels/Data_raw/Level2Ecoregions' 
##   using driver `ESRI Shapefile'
## Simple feature collection with 2261 features and 8 fields
## Geometry type: POLYGON
## Dimension:     XY
## Bounding box:  xmin: -4334052 ymin: -3313739 xmax: 3324076 ymax: 4267265
## Projected CRS: Sphere_ARC_INFO_Lambert_Azimuthal_Equal_Area

regions <- regions %>% 
  st_transform(crs = st_crs(crs(test_rast))) %>% 
  st_make_valid() 

ecoregionLU <- data.frame("NA_L1NAME" = sort(unique(regions$NA_L1NAME)), 
                        "newRegion" = c(NA, "Forest", "dryShrubGrass", 
                                        "dryShrubGrass", "Forest", "dryShrubGrass",
                                       "dryShrubGrass", "Forest", "Forest", 
                                       "dryShrubGrass", "Forest", "Forest", 
                                       "Forest", "Forest", "dryShrubGrass", 
                                       NA
                                        ))
goodRegions <- regions %>% 
  left_join(ecoregionLU)
mapRegions <- goodRegions %>% 
  filter(!is.na(newRegion)) %>% 
  group_by(newRegion) %>% 
  summarise(geometry = sf::st_union(geometry)) %>% 
  ungroup() %>% 
  st_simplify(dTolerance = 1000) %>% 
  sf::st_crop(c("xmin" = -2000000, "xmax" = 2600000, "ymin" = -1900000, "ymax" = 1500000))
# make shapefile of cropped state boundaries in appropriate crs
cropped_states_2 <- cropped_states %>% 
  st_transform(crs = crs(test_rast)) %>% 
  st_make_valid()  %>% 
  sf::st_crop(c("xmin" = -2000000, "xmax" = 2600000, "ymin" = -1900000, "ymax" = 1500000))

# function for getting the statistical mode
Mode <- function(x, ...) {
  ux <- unique(x)
  ux[which.max(tabulate(match(x, ux)))]
}

# make a multi-layer raster w/ layers for each variable of interest
pred_glm1_full_sf <- pred_glm1_full %>% 
  st_as_sf(coords = c("x", "y"), crs = crs("EPSG:4326")) %>% 
  st_transform(crs(test_rast)) %>% 
  terra::vect()
testRast2 <- lapply(c("TotalTreeCover", "TotalTreeCover_binom", "TotalTreeCover_binom_pred", "TotalTreeCover_binom_pred_binary", "resid", "missClass"), FUN = function(x) {
  # S4 method for class 'data.frame'
  if (x %in% c("TotalTreeCover", "TotalTreeCover_binom", "TotalTreeCover_binom_pred", "TotalTreeCover_binom_pred_binary", "resid")) {
    temp <- terra::rasterize(x = pred_glm1_full_sf, y = test_rast, 
                         field = x, fun = mean, na.rm = TRUE)
    names(temp) <- x
  } else {
    temp <- terra::rasterize(x = pred_glm1_full_sf, y = test_rast, 
                         field = x, fun = Mode, na.rm = TRUE)
    # get the % aggreement between values in the dayMetx8 cell 
    temp2 <- terra::rasterize(x = pred_glm1_full_sf, y = test_rast$daymet_v4_prcp_monttl_na_1980_1, 
                         field = x, fun = function(y) {
                           yTemp <- y[!is.na(y)]
                           yMode <- Mode(yTemp)
                           (sum(yTemp == yMode)/length(yTemp))*100
                         })
    temp <- c(as.factor(temp$missClass), temp2)
    names(temp) <- c("missClass", "PercAgreement")
  }
    
 return(temp)
  }
)
pred_glm1_full_RAST <- c(testRast2[[1]], testRast2[[2]], testRast2[[3]], testRast2[[4]], testRast2[[5]], testRast2[[6]])

# ## compare
# par(mfrow = c(2,1))
# terra::plot(pred_glm1_full_RAST$TotalTreeCover,  maxcell = 30000000, main = "gridMet")
# terra::plot(pred_glm1_full_RAST_dayMet$TotalTreeCover, maxcell = 30000000, main = "dayMet")
# par(mfrow = c(1,1))
##
# make figure of raw tree cover
map_obs_cont <- ggplot() +
geom_spatraster(data = pred_glm1_full_RAST, aes(fill = TotalTreeCover), maxcell = 50000000) + 
 #geom_sf(data = pred_glm1_full_RAST, aes(col = TotalTreeCover)) + 
  # stat_summary_2d(data = plotObs, aes(x = x, y = y, z = TotalTreeCover), fun = mean, binwidth = .05) + 
  geom_sf(data=cropped_states_2 ,fill=NA ) +
  geom_sf(data = mapRegions, fill = NA, col = "orchid", lwd = .5) +
labs(title = paste0("Observations of Continuous Total Tree Cover - all data")) +
  scale_fill_gradient2(low = "brown",
                       mid = "wheat" ,
                       high = "forestgreen" , 
                       midpoint = 0,   na.value = "white") + 
  coord_sf(datum = st_crs(pred_glm1_full_RAST)) +
   # xlim(-104, -100) + 
   # ylim(30, 33)
  xlim(-2000000, 2500000) + 
  ylim(-1800000, 900000)

# make figure of binomialized tree cover
map_obs <- ggplot() +
geom_spatraster(data = pred_glm1_full_RAST, aes(fill = TotalTreeCover_binom), maxcell = 50000000) + 
 #geom_sf(data = plotObs, aes(col = TotalTreeCover_binom)) + 
   #stat_summary_2d(data = plotObs, aes(x = x, y = y, z = TotalTreeCover_binom), fun = mean, binwidth = .05) + 
     scale_fill_viridis_c(option = "A", guide = guide_colorbar(title = "% cover"), 
                          limits = c(0,100))  +
  geom_sf(data=cropped_states_2 ,fill=NA ) +
  geom_sf(data = mapRegions, fill = NA, col = "orchid", lwd = .5) +
labs(title = paste0("Observations of Binomial Total Tree Cover - all data")) +
  scale_fill_continuous(breaks =  c(0, 0.5, 1), palette = c("wheat", "forestgreen"),
                    labels = c("No Trees",
                               "",
                      "Trees"), na.value = "white") + 
  coord_sf(datum = st_crs(pred_glm1_full_RAST)) +
  xlim(-2000000, 2500000) + 
  ylim(-1800000, 900000)

hist_obs_cont <- pred_glm1_full %>% 
  ggplot() + 
  geom_histogram(aes(TotalTreeCover), fill = "lightgrey", col = "darkgrey")

hist_obs <- pred_glm1_full%>% 
  ggplot() + 
  geom_histogram(aes(TotalTreeCover_binom), fill = "lightgrey", col = "darkgrey")

library(ggpubr)
ggarrange(map_obs_cont, hist_obs_cont, map_obs, hist_obs, heights = c(3, 1, 3, 1), ncol = 1)

Observations - continuous and binary total tree cover for the test dataset

pred_glm1_test_sf <- pred_glm1_test %>% 
  st_as_sf(coords = c("x", "y"), crs = crs("EPSG:4326")) %>% 
  st_transform(crs(test_rast)) %>% 
  terra::vect()
# make raster of test set 
# make a multi-layer raster w/ layers for each variable of interest
testRast_test <- lapply(c("TotalTreeCover", "TotalTreeCover_binom", "TotalTreeCover_binom_pred", "TotalTreeCover_binom_pred_binary", "resid", "missClass"), FUN = function(x) {
  # S4 method for class 'data.frame'
  if (x %in% c("TotalTreeCover", "TotalTreeCover_binom", "TotalTreeCover_binom_pred", "TotalTreeCover_binom_pred_binary", "resid")) {
    temp <- terra::rasterize(x = pred_glm1_test_sf, y = test_rast, 
                         field = x, fun = mean, na.rm = TRUE)
    names(temp) <- x
  } else {
    temp <- terra::rasterize(x = pred_glm1_test_sf, y = test_rast, 
                         field = x, fun = Mode, na.rm = TRUE)
    # get the % aggreement between values in the dayMetx8 cell 
    temp2 <- terra::rasterize(x = pred_glm1_test_sf, y = test_rast$daymet_v4_prcp_monttl_na_1980_1, 
                         field = x, fun = function(y) {
                           yTemp <- y[!is.na(y)]
                           yMode <- Mode(yTemp)
                           (sum(yTemp == yMode)/length(yTemp))*100
                         })
    temp <- c(as.factor(temp$missClass), temp2)
    names(temp) <- c("missClass", "PercAgreement")
  }
    
 return(temp)
  }
)
pred_glm1_test_RAST <- c(testRast_test[[1]], testRast_test[[2]], testRast_test[[3]], testRast_test[[4]], testRast_test[[5]], testRast_test[[6]])

# make maps 
map_obs_cont_test <- ggplot() +
geom_spatraster(data = pred_glm1_test_RAST, aes(fill = TotalTreeCover), maxcell = 50000000) + 
 #geom_sf(data = pred_glm1_full_RAST, aes(col = TotalTreeCover)) + 
  # stat_summary_2d(data = plotObs, aes(x = x, y = y, z = TotalTreeCover), fun = mean, binwidth = .05) + 
  geom_sf(data=cropped_states_2 ,fill=NA ) +
  geom_sf(data = mapRegions, fill = NA, col = "orchid", lwd = .5) +
labs(title = paste0("Observations of Continuous Total Tree Cover - test data")) +
  scale_fill_gradient2(low = "brown",
                       mid = "wheat" ,
                       high = "forestgreen" , 
                       midpoint = 0,   na.value = "white") + 
  coord_sf(datum = st_crs(pred_glm1_full_RAST)) +
   # xlim(-104, -100) + 
   # ylim(30, 33)
  xlim(-2000000, 2500000) + 
  ylim(-1800000, 900000)

# make figure of binomialized tree cover
map_obs_test <- ggplot() +
geom_spatraster(data = pred_glm1_test_RAST, aes(fill = TotalTreeCover_binom), maxcell = 50000000) + 
 #geom_sf(data = plotObs, aes(col = TotalTreeCover_binom)) + 
   #stat_summary_2d(data = plotObs, aes(x = x, y = y, z = TotalTreeCover_binom), fun = mean, binwidth = .05) + 
     scale_fill_viridis_c(option = "A", guide = guide_colorbar(title = "% cover"), 
                          limits = c(0,100))  +
  geom_sf(data=cropped_states_2 ,fill=NA ) +
  geom_sf(data = mapRegions, fill = NA, col = "orchid", lwd = .5) +
labs(title = paste0("Observations of Binomial Total Tree Cover - test data")) +
  scale_fill_continuous(breaks =  c(0, 0.5, 1), palette = c("wheat", "forestgreen"),
                    labels = c("No Trees",
                               "",
                      "Trees"), na.value = "white") + 
  coord_sf(datum = st_crs(pred_glm1_full_RAST)) +
  xlim(-2000000, 2500000) + 
  ylim(-1800000, 900000)

hist_obs_cont_test <- pred_glm1_test %>% 
  ggplot() + 
  geom_histogram(aes(TotalTreeCover), fill = "lightgrey", col = "darkgrey")

  hist_obs_test <- pred_glm1_test%>% 
  ggplot() + 
  geom_histogram(aes(TotalTreeCover_binom), fill = "lightgrey", col = "darkgrey")

ggarrange(map_obs_cont_test, hist_obs_cont_test, map_obs_test, hist_obs_test, heights = c(3, 1, 3, 1), ncol = 1)

Predictions on the full and test dataset using the best lambda model

# make figures of predictions w/ the full dataset
map_preds1_cont <- ggplot() +
geom_spatraster(data = pred_glm1_full_RAST, aes(fill = TotalTreeCover_binom_pred), maxcell = 20000000) + 
 #geom_sf(data = plotObs_rast2, aes(col = TotalTreeCover)) + 
  # stat_summary_2d(data = plotObs, aes(x = x, y = y, z = TotalTreeCover), fun = mean, binwidth = .05) + 
  geom_sf(data=cropped_states_2 ,fill=NA ) +
  geom_sf(data = mapRegions, fill = NA, col = "orchid", lwd = .5) +
labs(title = paste0("Predictions from the bestaLambda model of Yes/No Trees \ncontinuous probabilities \nfull dataset")) +
  scale_fill_gradient2(low = "brown",
                       mid = "wheat" ,
                       high = "forestgreen" , 
                       midpoint = 0,   na.value = "white") + 
  coord_sf(datum = st_crs(pred_glm1_full_RAST)) +
  xlim(-2000000, 2500000) + 
  ylim(-1800000, 900000)

# make figure of binomialized tree cover
map_preds1 <- ggplot() +
geom_spatraster(data = pred_glm1_full_RAST, aes(fill = TotalTreeCover_binom_pred_binary), maxcell = 20000000) + 
 #geom_sf(data = plotObs, aes(col = TotalTreeCover_binom)) + 
   #stat_summary_2d(data = plotObs, aes(x = x, y = y, z = TotalTreeCover_binom), fun = mean, binwidth = .05) + 
     scale_fill_viridis_c(option = "A", guide = guide_colorbar(title = "% cover"), 
                          limits = c(0,100))  +
  geom_sf(data=cropped_states_2 ,fill=NA ) +
  geom_sf(data = mapRegions, fill = NA, col = "orchid", lwd = .5) +
labs(title = paste0("Predictions from the bestaLambda model of Yes/No Trees \nbinary probabilities \nfull dataset")) +
  scale_fill_continuous(breaks =  c(0, 0.5, 1), palette = c("wheat", "forestgreen"),
                    labels = c("No Trees",
                               "",
                      "Trees"), na.value = "white") + 
  coord_sf(datum = st_crs(pred_glm1_full_RAST)) +
  xlim(-2000000, 2500000) + 
  ylim(-1800000, 900000)

hist_preds1_cont <- pred_glm1_full %>% 
  ggplot() + 
  geom_histogram(aes(TotalTreeCover_binom_pred), fill = "lightgrey", col = "darkgrey")

hist_preds1 <- pred_glm1_full%>% 
  ggplot() + 
  geom_histogram(aes(TotalTreeCover_binom_pred_binary), fill = "lightgrey", col = "darkgrey")

ggarrange(map_preds1_cont, hist_preds1_cont, map_preds1, hist_preds1, heights = c(3, 1, 3, 1), ncol = 1)

# make figures of predictions w/ the test dataset
map_preds1_cont_test <- ggplot() +
geom_spatraster(data = pred_glm1_test_RAST, aes(fill = TotalTreeCover_binom_pred), maxcell = 20000000) + 
 #geom_sf(data = plotObs_rast2, aes(col = TotalTreeCover)) + 
  # stat_summary_2d(data = plotObs, aes(x = x, y = y, z = TotalTreeCover), fun = mean, binwidth = .05) + 
  geom_sf(data=cropped_states_2 ,fill=NA ) +
  geom_sf(data = mapRegions, fill = NA, col = "orchid", lwd = .5) +
labs(title = paste0("Predictions from the bestaLambda model of Yes/No Trees \ncontinuous probabilities \ntest dataset")) +
  scale_fill_gradient2(low = "brown",
                       mid = "wheat" ,
                       high = "forestgreen" , 
                       midpoint = 0,   na.value = "white") + 
  coord_sf(datum = st_crs(pred_glm1_full_RAST)) +
  xlim(-2000000, 2500000) + 
  ylim(-1800000, 900000)

# make figure of binomialized tree cover
map_preds1_test <- ggplot() +
geom_spatraster(data = pred_glm1_test_RAST, aes(fill = TotalTreeCover_binom_pred_binary), maxcell = 20000000) + 
 #geom_sf(data = plotObs, aes(col = TotalTreeCover_binom)) + 
   #stat_summary_2d(data = plotObs, aes(x = x, y = y, z = TotalTreeCover_binom), fun = mean, binwidth = .05) + 
     scale_fill_viridis_c(option = "A", guide = guide_colorbar(title = "% cover"), 
                          limits = c(0,100))  +
  geom_sf(data=cropped_states_2 ,fill=NA ) +
  geom_sf(data = mapRegions, fill = NA, col = "orchid", lwd = .5) +
labs(title = paste0("Predictions from the bestaLambda model of Yes/No Trees \nbinary probabilities \ntest dataset")) +
  scale_fill_continuous(breaks =  c(0, 0.5, 1), palette = c("wheat", "forestgreen"),
                    labels = c("No Trees",
                               "",
                      "Trees"), na.value = "white") + 
  coord_sf(datum = st_crs(pred_glm1_full_RAST)) +
  xlim(-2000000, 2500000) + 
  ylim(-1800000, 900000)

hist_preds1_cont_test <- pred_glm1_test %>% 
  ggplot() + 
  geom_histogram(aes(TotalTreeCover_binom_pred), fill = "lightgrey", col = "darkgrey")

hist_preds1_test <- pred_glm1_test%>% 
  ggplot() + 
  geom_histogram(aes(TotalTreeCover_binom_pred_binary), fill = "lightgrey", col = "darkgrey")

ggarrange(map_preds1_cont_test, hist_preds1_cont_test, map_preds1_test, hist_preds1_test, heights = c(3, 1, 3, 1), ncol = 1)

Predictions on the full and test datasets using the second best lambda model

if ( name_secondBestMod == "Intercept_Only") {
  print("The next best lambda model only contains one predictor (an intercept)")
} else {
  pred_glm1_1se_full_sf <- pred_glm1_1se_full %>% 
  st_as_sf(coords = c("x", "y"), crs = crs("EPSG:4326")) %>% 
  st_transform(crs(test_rast)) %>% 
  terra::vect()
  # make a raster of the full dataset
# make a multi-layer raster w/ layers for each variable of interest
testRast3 <- lapply(c("TotalTreeCover", "TotalTreeCover_binom", "TotalTreeCover_binom_pred", "TotalTreeCover_binom_pred_binary", "resid", "missClass"), FUN = function(x) {
  # S4 method for class 'data.frame'
 if (x %in% c("TotalTreeCover", "TotalTreeCover_binom", "TotalTreeCover_binom_pred", "TotalTreeCover_binom_pred_binary", "resid")) {
    temp <- terra::rasterize(x = pred_glm1_1se_full_sf, y = test_rast, 
                         field = x, fun = mean, na.rm = TRUE)
    names(temp) <- x
  } else {
    temp <- terra::rasterize(x = pred_glm1_1se_full_sf, y = test_rast, 
                         field = x, fun = Mode, na.rm = TRUE)
    # get the % aggreement between values in the dayMetx8 cell 
    temp2 <- terra::rasterize(x = pred_glm1_1se_full_sf, y = test_rast$daymet_v4_prcp_monttl_na_1980_1, 
                         field = x, fun = function(y) {
                           yTemp <- y[!is.na(y)]
                           yMode <- Mode(yTemp)
                           (sum(yTemp == yMode)/length(yTemp))*100
                         })
    temp <- c(as.factor(temp$missClass), temp2)
    names(temp) <- c("missClass", "PercAgreement")
  }
    
 return(temp)
  }
)
pred_glm1_1se_full_RAST <- c(testRast3[[1]], testRast3[[2]], testRast3[[3]], testRast3[[4]], testRast3[[5]], testRast3[[6]])

# make raster of test set 
 pred_glm1_1se_test_sf <- pred_glm1_1se_test %>% 
  st_as_sf(coords = c("x", "y"), crs = crs("EPSG:4326")) %>% 
  st_transform(crs(test_rast)) %>% 
  terra::vect()
# make a multi-layer raster w/ layers for each variable of interest
testRast_test2 <- lapply(c("TotalTreeCover", "TotalTreeCover_binom", "TotalTreeCover_binom_pred", "TotalTreeCover_binom_pred_binary", "resid", "missClass"), FUN = function(x) {
  # S4 method for class 'data.frame'
 if (x %in% c("TotalTreeCover", "TotalTreeCover_binom", "TotalTreeCover_binom_pred", "TotalTreeCover_binom_pred_binary", "resid")) {
    temp <- terra::rasterize(x = pred_glm1_1se_test_sf, y = test_rast, 
                         field = x, fun = mean, na.rm = TRUE)
    names(temp) <- x
  } else {
    temp <- terra::rasterize(x = pred_glm1_1se_test_sf, y = test_rast, 
                         field = x, fun = Mode, na.rm = TRUE)
    # get the % aggreement between values in the dayMetx8 cell 
    temp2 <- terra::rasterize(x = pred_glm1_1se_test_sf, y = test_rast$daymet_v4_prcp_monttl_na_1980_1, 
                         field = x, fun = function(y) {
                           yTemp <- y[!is.na(y)]
                           yMode <- Mode(yTemp)
                           (sum(yTemp == yMode)/length(yTemp))*100
                         })
    temp <- c(as.factor(temp$missClass), temp2)
    names(temp) <- c("missClass", "PercAgreement")
  }
    
 return(temp)
  }
)
pred_glm1_1se_test_RAST <- c(testRast_test2[[1]], testRast_test2[[2]], testRast_test2[[3]], testRast_test2[[4]], testRast_test2[[5]], testRast_test2[[6]])

# make figures of predictions w/ the full dataset
map_preds2_cont <- ggplot() +
geom_spatraster(data = pred_glm1_1se_full_RAST, aes(fill = TotalTreeCover_binom_pred), maxcell = 20000000) + 
 #geom_sf(data = plotObs_rast2, aes(col = TotalTreeCover)) + 
  # stat_summary_2d(data = plotObs, aes(x = x, y = y, z = TotalTreeCover), fun = mean, binwidth = .05) + 
  geom_sf(data=cropped_states_2 ,fill=NA ) +
  geom_sf(data = mapRegions, fill = NA, col = "orchid", lwd = .5) +
labs(title = paste0("Predictions from the ", name_secondBestMod, " of Yes/No Trees \ncontinuous probabilities \nfull dataset")) +
  scale_fill_gradient2(low = "brown",
                       mid = "wheat" ,
                       high = "forestgreen" , 
                       midpoint = 0,   na.value = "white") + 
  coord_sf(datum = st_crs(pred_glm1_full_RAST)) +
  xlim(-2000000, 2500000) + 
  ylim(-1800000, 900000)

# make figure of binomialized tree cover
map_preds2 <- ggplot() +
geom_spatraster(data = pred_glm1_1se_full_RAST, aes(fill = TotalTreeCover_binom_pred_binary), maxcell = 20000000) + 
 #geom_sf(data = plotObs, aes(col = TotalTreeCover_binom)) + 
   #stat_summary_2d(data = plotObs, aes(x = x, y = y, z = TotalTreeCover_binom), fun = mean, binwidth = .05) + 
  geom_sf(data=cropped_states_2 ,fill=NA ) +
  geom_sf(data = mapRegions, fill = NA, col = "orchid", lwd = .5) +
labs(title = paste0("Predictions from the ", name_secondBestMod, " of Yes/No Trees \nbinary probabilities \nfull dataset")) +
  scale_fill_continuous(breaks =  c(0, 0.5, 1), palette = c("wheat", "forestgreen"),
                    labels = c("No Trees",
                               "",
                      "Trees"), na.value = "white") + 
  coord_sf(datum = st_crs(pred_glm1_full_RAST)) +
  xlim(-2000000, 2500000) + 
  ylim(-1800000, 900000)

hist_preds2_cont <- pred_glm1_1se_full %>% 
  ggplot() + 
  geom_histogram(aes(TotalTreeCover_binom_pred), fill = "lightgrey", col = "darkgrey")

hist_preds2 <- pred_glm1_1se_full%>% 
  ggplot() + 
  geom_histogram(aes(TotalTreeCover_binom_pred_binary), fill = "lightgrey", col = "darkgrey")


# make figures of predictions w/ the test dataset
map_preds2_cont_test <- ggplot() +
geom_spatraster(data = pred_glm1_1se_test_RAST, aes(fill = TotalTreeCover_binom_pred), maxcell = 20000000) + 
 #geom_sf(data = plotObs_rast2, aes(col = TotalTreeCover)) + 
  # stat_summary_2d(data = plotObs, aes(x = x, y = y, z = TotalTreeCover), fun = mean, binwidth = .05) + 
  geom_sf(data=cropped_states_2 ,fill=NA ) +
  geom_sf(data = mapRegions, fill = NA, col = "orchid", lwd = .5) +
labs(title = paste0("Predictions from the ", name_secondBestMod, " of Yes/No Trees \ncontinuous probabilities \ntest dataset")) +
  scale_fill_gradient2(low = "brown",
                       mid = "wheat" ,
                       high = "forestgreen" , 
                       midpoint = 0,   na.value = "white") +
  coord_sf(datum = st_crs(pred_glm1_full_RAST)) +
  xlim(-2000000, 2500000) + 
  ylim(-1800000, 900000)

# make figure of binomialized tree cover
map_preds2_test <- ggplot() +
geom_spatraster(data = pred_glm1_1se_test_RAST, aes(fill = TotalTreeCover_binom_pred_binary), maxcell = 20000000) + 
 #geom_sf(data = plotObs, aes(col = TotalTreeCover_binom)) + 
   #stat_summary_2d(data = plotObs, aes(x = x, y = y, z = TotalTreeCover_binom), fun = mean, binwidth = .05) + 
  geom_sf(data=cropped_states_2 ,fill=NA ) +
  geom_sf(data = mapRegions, fill = NA, col = "orchid", lwd = .5) +
labs(title = paste0("Predictions from the ", name_secondBestMod, " of Yes/No Trees \nbinary probabilities \ntest dataset")) +
  scale_fill_continuous(breaks =  c(0, 0.5, 1), palette = c("wheat", "forestgreen"),
                    labels = c("No Trees",
                               "",
                      "Trees"), na.value = "white") + 
  coord_sf(datum = st_crs(pred_glm1_full_RAST)) +
  xlim(-2000000, 2500000) + 
  ylim(-1800000, 900000)

hist_preds2_cont_test <- pred_glm1_1se_test %>% 
  ggplot() + 
  geom_histogram(aes(TotalTreeCover_binom_pred), fill = "lightgrey", col = "darkgrey")

hist_preds2_test <- pred_glm1_1se_test%>% 
  ggplot() + 
  geom_histogram(aes(TotalTreeCover_binom_pred_binary), fill = "lightgrey", col = "darkgrey")

ggarrange(ggarrange(map_preds2_cont, hist_preds2_cont, map_preds2, hist_preds2, heights = c(3, 1, 3, 1), ncol = 1),
ggarrange(map_preds2_cont_test, hist_preds2_cont_test, map_preds2_test, hist_preds2_test, heights = c(3, 1, 3, 1), ncol = 1),
ncol = 1
)
}

A map of classification error of predictions on the full and test datasets made using the best lambda model

# true positive = tree (1) (forest green)
# true negative = no tree (3) (wheat) 
# false positive = model says tree, data says no-tree (2) (red)
# false negative = model says no tree, data says tree (4) (blue)
# make figures
map_missClass <- ggplot() +
geom_spatraster(data =pred_glm1_full_RAST
                , aes(fill= missClass), maxcell = 20000000) + 
    #stat_summary_2d(data = pred_glm1, aes(x = x, y = y, z = missClass), fun = function(x) {round(mean(x))}, binwidth = .05) + 
  geom_sf(data=cropped_states_2,fill=NA )  + 
  geom_sf(data = mapRegions, fill = NA, col = "orchid", lwd = .5) +
  #geom_sf(data = badResids_high, col = "blue") +
  #geom_sf(data = badResids_low, col = "red") +
labs(title = paste0("Misclassification and correct classifications \nfrom the bestLambda model of Yes/No Trees \nfull dataset"),
     subtitle = "bestLambda model \nvalues show are the most common classification in each 8km x 8km grid cell") +
    scale_fill_discrete(palette = 
                        c("forestgreen", "red", "wheat", "blue"),
                        na.value = "white",
                        labels = c("forest", "Data = no trees; Model = trees", "non-forest", "Data = trees; Model = no trees", "")) +
  coord_sf(datum = st_crs(pred_glm1_full_RAST)) +
  xlim(-2000000, 2500000) + 
  ylim(-1800000, 900000)
# make a map of the aggreement in classification w/in each 8x8km cell 
map_missClass_ag <- ggplot() +
  geom_spatraster(data = pred_glm1_full_RAST, aes(fill= PercAgreement), maxcell = 20000000) + 
    #stat_summary_2d(data = pred_glm1, aes(x = x, y = y, z = missClass), fun = function(x) {round(mean(x))}, binwidth = .05) + 
  geom_sf(data=cropped_states_2,fill=NA )  + 
  geom_sf(data = mapRegions, fill = NA, col = "orchid", lwd = .5) +
  #geom_sf(data = badResids_high, col = "blue") +
  #geom_sf(data = badResids_low, col = "red") +
labs(title = paste0("% Agreement of the classification values within each 8x8km^2 gridcell \nclassifications using the bestLambda model of Yes/No Trees \nfull dataset"))+
    scale_fill_viridis_c(option = "B", na.value = "white", name = "% agreement", ) +
  coord_sf(datum = st_crs(pred_glm1_full_RAST)) +
  xlim(-2000000, 2500000) + 
  ylim(-1800000, 900000)

ggarrange(map_missClass, map_missClass_ag, ncol = 1, heights = c(1, .7), align = "v")

# make a confusion matrix 
# prepare data
matData <- pred_glm1_full %>% 
  mutate(predClass = TotalTreeCover_binom_pred_binary, 
         obsClass = TotalTreeCover_binom) %>% 
  mutate(predClass = replace(predClass, predClass == 0, "no trees"),
         predClass = replace(predClass, predClass == 1, "trees"),
         obsClass = replace(obsClass, obsClass == 0, "no trees"),
         obsClass = replace(obsClass, obsClass == 1, "trees")) %>% 
mutate(predClass = as.factor(predClass) ,
       obsClass = as.factor(obsClass))

# make matrix as a data.frame
# confMat <-  confusionMatrix(data = matData$predClass,
#                  reference = matData$obsClass)
ConfusionTableR::binary_visualiseR(
  train_labels = as.factor(matData$predClass),
  truth_labels = as.factor(matData$obsClass),
   class_label1 = "No trees",
   class_label2 = "Trees",
   quadrant_col1 = "wheat",
   quadrant_col2 = "forestgreen",
  text_col = "white", custom_title = "Confusion Matrix: classification of full dataset \nwith the best lambda model  using the full dataset"
)

### test dataset

# make figures
map_missClass_test <- ggplot() +
geom_spatraster(data =pred_glm1_test_RAST, aes(fill= missClass), maxcell = 20000000) + 
    #stat_summary_2d(data = pred_glm1, aes(x = x, y = y, z = missClass), fun = function(x) {round(mean(x))}, binwidth = .05) + 
  geom_sf(data=cropped_states_2,fill=NA )  + 
  geom_sf(data = mapRegions, fill = NA, col = "orchid", lwd = .5) +
  #geom_sf(data = badResids_high, col = "blue") +
  #geom_sf(data = badResids_low, col = "red") +
labs(title = paste0("Misclassification and correct classifications \nfrom the bestLambda model of Yes/No Trees \ntest dataset"),
     subtitle = "bestLambda model \nvalues show are the most common classification in each 8km x 8km grid cell") +
    scale_fill_discrete(palette = 
                        c("forestgreen", "red", "wheat", "blue"),
                        na.value = "white",
                        labels = c("forest", "Data = no trees; Model = trees", "non-forest", "Data = trees; Model = no trees", "")) +
  coord_sf(datum = st_crs(pred_glm1_full_RAST)) +
  xlim(-2000000, 2500000) + 
  ylim(-1800000, 900000)
map_missClass_test_ag <- ggplot() +
  geom_spatraster(data = pred_glm1_test_RAST, aes(fill= PercAgreement), maxcell = 20000000) + 
    #stat_summary_2d(data = pred_glm1, aes(x = x, y = y, z = missClass), fun = function(x) {round(mean(x))}, binwidth = .05) + 
  geom_sf(data=cropped_states_2,fill=NA )  + 
  geom_sf(data = mapRegions, fill = NA, col = "orchid", lwd = .5) +
  #geom_sf(data = badResids_high, col = "blue") +
  #geom_sf(data = badResids_low, col = "red") +
labs(title = paste0("% Agreement of the classification values within each 8x8km^2 gridcell \nclassifications using the bestLambda model of Yes/No Trees \ntest dataset"))+
    scale_fill_viridis_c(option = "B", na.value = "white", name = "% agreement", ) +
  coord_sf(datum = st_crs(pred_glm1_full_RAST)) +
  xlim(-2000000, 2500000) + 
  ylim(-1800000, 900000)
  

  ggarrange(map_missClass_test, map_missClass_test_ag, ncol = 1, heights = c(1, .7), align = "v")

# make a confusion matrix 
# prepare data
matData_test <- pred_glm1_test %>% 
  mutate(predClass = TotalTreeCover_binom_pred_binary, 
         obsClass = TotalTreeCover_binom) %>% 
  mutate(predClass = replace(predClass, predClass == 0, "no trees"),
         predClass = replace(predClass, predClass == 1, "trees"),
         obsClass = replace(obsClass, obsClass == 0, "no trees"),
         obsClass = replace(obsClass, obsClass == 1, "trees")) %>% 
mutate(predClass = as.factor(predClass) ,
       obsClass = as.factor(obsClass))

# make matrix as a data.frame
# confMat <-  confusionMatrix(data = matData$predClass,
#                  reference = matData$obsClass)
ConfusionTableR::binary_visualiseR(
  train_labels = as.factor(matData_test$predClass),
  truth_labels = as.factor(matData_test$obsClass),
   class_label1 = "No trees",
   class_label2 = "Trees",
   quadrant_col1 = "wheat",
   quadrant_col2 = "forestgreen",
  text_col = "white", custom_title = "Confusion Matrix: classification of test dataset \nwith the best lambda model using the test dataset"
)

A map of classification error of predictions on the full and test datasets made using the second best lambda model

### full dataset
# make figures
map_missClass <- ggplot() +
geom_spatraster(data =pred_glm1_1se_full_RAST, aes(fill= missClass), maxcell = 20000000) + 
    #stat_summary_2d(data = pred_glm1, aes(x = x, y = y, z = missClass), fun = function(x) {round(mean(x))}, binwidth = .05) + 
  geom_sf(data=cropped_states_2,fill=NA )  + 
  geom_sf(data = mapRegions, fill = NA, col = "orchid", lwd = .5) +
  #geom_sf(data = badResids_high, col = "blue") +
  #geom_sf(data = badResids_low, col = "red") +
labs(title = paste0("Misclassification and correct classifications \nfrom the second-best lambda model of Yes/No Trees \nfull dataset"),
     subtitle = "second-best lambda model \nvalues show are the most common classification in each 8km x 8km grid cell") + 
  scale_fill_discrete(palette = 
                        c("forestgreen", "red", "wheat", "blue"),
                        na.value = "white",
                        labels = c("forest", "Data = no trees; Model = trees", "non-forest", "Data = trees; Model = no trees", "")) +
  coord_sf(datum = st_crs(pred_glm1_full_RAST)) +
  xlim(-2000000, 2500000) + 
  ylim(-1800000, 900000)
map_missClass_ag <- ggplot() +
  geom_spatraster(data = pred_glm1_1se_full_RAST, aes(fill= PercAgreement), maxcell = 20000000) + 
    #stat_summary_2d(data = pred_glm1, aes(x = x, y = y, z = missClass), fun = function(x) {round(mean(x))}, binwidth = .05) + 
  geom_sf(data=cropped_states_2,fill=NA )  + 
  geom_sf(data = mapRegions, fill = NA, col = "orchid", lwd = .5) +
  #geom_sf(data = badResids_high, col = "blue") +
  #geom_sf(data = badResids_low, col = "red") +
labs(title = paste0("% Agreement of the classification values within each 8x8km^2 gridcell \nclassifications using the second-best lambda model of Yes/No Trees \nfull dataset"))+
    scale_fill_viridis_c(option = "B", na.value = "white", name = "% agreement", ) +
  coord_sf(datum = st_crs(pred_glm1_full_RAST)) +
  xlim(-2000000, 2500000) + 
  ylim(-1800000, 900000)
  
ggarrange(map_missClass, map_missClass_ag, ncol = 1, heights = c(1, .7), align = "v")

# make a confusion matrix 
# prepare data
matData <- pred_glm1_1se_full %>% 
  mutate(predClass = TotalTreeCover_binom_pred_binary, 
         obsClass = TotalTreeCover_binom) %>% 
  mutate(predClass = replace(predClass, predClass == 0, "no trees"),
         predClass = replace(predClass, predClass == 1, "trees"),
         obsClass = replace(obsClass, obsClass == 0, "no trees"),
         obsClass = replace(obsClass, obsClass == 1, "trees")) %>% 
mutate(predClass = as.factor(predClass) ,
       obsClass = as.factor(obsClass))

# make matrix as a data.frame
# confMat <-  confusionMatrix(data = matData$predClass,
#                  reference = matData$obsClass)
ConfusionTableR::binary_visualiseR(
  train_labels = as.factor(matData$predClass),
  truth_labels = as.factor(matData$obsClass),
   class_label1 = "No trees",
   class_label2 = "Trees",
   quadrant_col1 = "wheat",
   quadrant_col2 = "forestgreen",
  text_col = "white", custom_title = "Confusion Matrix: classification of full dataset \nwith the second-best lambda model using the full dataset"
)

### test dataset
# make figures
map_missClass_test <- ggplot() +
geom_spatraster(data =pred_glm1_1se_test_RAST, aes(fill= missClass), maxcell = 20000000) + 
    #stat_summary_2d(data = pred_glm1, aes(x = x, y = y, z = missClass), fun = function(x) {round(mean(x))}, binwidth = .05) + 
  geom_sf(data=cropped_states_2,fill=NA )  + 
  geom_sf(data = mapRegions, fill = NA, col = "orchid", lwd = .5) +
  #geom_sf(data = badResids_high, col = "blue") +
  #geom_sf(data = badResids_low, col = "red") +
labs(title = paste0("Misclassification and correct classifications \nfrom the second-best lambda model of Yes/No Trees \ntest dataset"),
     subtitle = "second-best lambda model \nvalues show are the most common classification in each 8km x 8km grid cell") +
     scale_fill_discrete(palette = 
                        c("forestgreen", "red", "wheat", "blue"),
                        na.value = "white",
                        labels = c("forest", "Data = no trees; Model = trees", "non-forest", "Data = trees; Model = no trees", "")) +
  coord_sf(datum = st_crs(pred_glm1_full_RAST)) +
  xlim(-2000000, 2500000) + 
  ylim(-1800000, 900000)

map_missClass_test_ag <- ggplot() +
  geom_spatraster(data = pred_glm1_1se_test_RAST, aes(fill= PercAgreement), maxcell = 20000000) + 
    #stat_summary_2d(data = pred_glm1, aes(x = x, y = y, z = missClass), fun = function(x) {round(mean(x))}, binwidth = .05) + 
  geom_sf(data=cropped_states_2,fill=NA )  + 
  geom_sf(data = mapRegions, fill = NA, col = "orchid", lwd = .5) +
  #geom_sf(data = badResids_high, col = "blue") +
  #geom_sf(data = badResids_low, col = "red") +
labs(title = paste0("% Agreement of the classification values within each 8x8km^2 gridcell \nclassifications using the second-best lambda model of Yes/No Trees \ntest dataset"))+
    scale_fill_viridis_c(option = "B", na.value = "white", name = "% agreement", ) +
  coord_sf(datum = st_crs(pred_glm1_full_RAST)) +
  xlim(-2000000, 2500000) + 
  ylim(-1800000, 900000)

  ggarrange(map_missClass_test, map_missClass_test_ag, ncol = 1, heights = c(1, .7), align = "v")

# make a confusion matrix 
# prepare data
matData_test <- pred_glm1_1se_test %>% 
  mutate(predClass = TotalTreeCover_binom_pred_binary, 
         obsClass = TotalTreeCover_binom) %>% 
  mutate(predClass = replace(predClass, predClass == 0, "no trees"),
         predClass = replace(predClass, predClass == 1, "trees"),
         obsClass = replace(obsClass, obsClass == 0, "no trees"),
         obsClass = replace(obsClass, obsClass == 1, "trees")) %>% 
mutate(predClass = as.factor(predClass) ,
       obsClass = as.factor(obsClass))

# make matrix as a data.frame
# confMat <-  confusionMatrix(data = matData$predClass,
#                  reference = matData$obsClass)
ConfusionTableR::binary_visualiseR(
  train_labels = as.factor(matData_test$predClass),
  truth_labels = as.factor(matData_test$obsClass),
   class_label1 = "No trees",
   class_label2 = "Trees",
   quadrant_col1 = "wheat",
   quadrant_col2 = "forestgreen",
  text_col = "white", custom_title = "Confusion Matrix: classification of test dataset \nwith the second-best lambda model using the test dataset"
)

Are there biases of the model predictions across year/lat/long? (for the full dataset)

if ( name_secondBestMod == "Intercept_Only") {
  print("The next best lambda model only contains one predictor (an intercept)")
  
  ## calculate Misclassification in the input pred_glm1 or pred_glm1se datasets
  pred_glm1_full$missClass2 <- pred_glm1_full$TotalTreeCover_binom - pred_glm1_full$TotalTreeCover_binom_pred_binary
  pred_glm1_test$missClass2 <- pred_glm1_test$TotalTreeCover_binom - pred_glm1_test$TotalTreeCover_binom_pred_binary

  # plot misclassifications against Year
yearResidMod_bestLambda <- ggplot(pred_glm1_full) + 
  geom_point(aes(x = jitter(Year), y = jitter(missClass2)), alpha = .1) + 
  geom_hline(aes(yintercept = 0), lty = 2, col = "red") + 
  geom_smooth(aes(x = Year, y = missClass2), method = "lm") + 
  xlab("Year") + 
  ylab("misclassifications") +
  ggtitle("from best lamba model")

# plot misclassifications against Lat
latResidMod_bestLambda <- ggplot(pred_glm1_full) + 
  geom_point(aes(x = y, y = jitter(missClass2)), alpha = .1) + 
  geom_hline(aes(yintercept = 0), lty = 2, col = "red") + 
  geom_smooth(aes(x = y, y = missClass2)) + 
  xlab("Latitude") + 
  ylab("misclassifications") +
  ggtitle("from best lamba model")

# plot misclassifications against Long
longResidMod_bestLambda <- ggplot(pred_glm1_full) + 
  geom_point(aes(x = x, y = jitter(missClass2)), alpha = .1) + 
  geom_hline(aes(yintercept = 0), lty = 2, col = "red") + 
  geom_smooth(aes(x = x, y = missClass2)) + 
  xlab("Longitude") + 
  ylab("misclassifications") +
  ggtitle("from best lamba model")
library(patchwork)
(yearResidMod_bestLambda ) / 
(  latResidMod_bestLambda ) /
(  longResidMod_bestLambda )
} else {
  
  ## calculate missClass2ification in the input pred_glm1 or pred_glm1se datasets
  pred_glm1_full$missClass2 <- pred_glm1_full$TotalTreeCover_binom - pred_glm1_full$TotalTreeCover_binom_pred_binary
  pred_glm1_test$missClass2 <- pred_glm1_test$TotalTreeCover_binom - pred_glm1_test$TotalTreeCover_binom_pred_binary
  pred_glm1_1se_full$missClass2 <- pred_glm1_1se_full$TotalTreeCover_binom - pred_glm1_1se_full$TotalTreeCover_binom_pred_binary
  pred_glm1_1se_test$missClass2 <- pred_glm1_1se_test$TotalTreeCover_binom - pred_glm1_1se_test$TotalTreeCover_binom_pred_binary

# plot misclassifications against Year
yearResidMod_bestLambda <- ggplot(pred_glm1_full) + 
  geom_point(aes(x = jitter(Year), y = jitter(missClass2)), alpha = .1) + 
  geom_hline(aes(yintercept = 0), lty = 2, col = "red") + 
  geom_smooth(aes(x = Year, y = missClass2), method = "lm") + 
  xlab("Year") + 
  ylab("misclassifications") +
  ggtitle("from best lamba model")
yearResidMod_1seLambda <- ggplot(pred_glm1_1se_full) + 
  geom_point(aes(x = jitter(Year), y = jitter(missClass2)), alpha = .1) + 
  geom_hline(aes(yintercept = 0), lty = 2, col = "red") + 
  geom_smooth(aes(x = Year, y = missClass2), method = "lm") + 
  xlab("Year") + 
  ylab("misclassifications") +
  ggtitle(paste0("from ", name_secondBestMod))

# plot misclassifications against Lat
latResidMod_bestLambda <- ggplot(pred_glm1_full) + 
  geom_point(aes(x = y, y = jitter(missClass2)), alpha = .1) + 
  geom_hline(aes(yintercept = 0), lty = 2, col = "red") + 
  geom_smooth(aes(x = y, y = missClass2)) + 
  xlab("Latitude") + 
  ylab("misclassifications") +
  ggtitle("from best lamba model")
latResidMod_1seLambda <- ggplot(pred_glm1_1se_full) + 
  geom_point(aes(x = y, y = jitter(missClass2)), alpha = .1) + 
  geom_hline(aes(yintercept = 0), lty = 2, col = "red") + 
  geom_smooth(aes(x = y, y = missClass2)) + 
  xlab("Latitude") + 
  ylab("misclassifications") +
  ggtitle(paste0("from ", name_secondBestMod))

# plot misclassifications against Long
longResidMod_bestLambda <- ggplot(pred_glm1_full) + 
  geom_point(aes(x = x, y = jitter(missClass2)), alpha = .1) + 
  geom_hline(aes(yintercept = 0), lty = 2, col = "red") + 
  geom_smooth(aes(x = x, y = missClass2)) + 
  xlab("Longitude") + 
  ylab("misclassifications") +
  ggtitle("from best lamba model")
longResidMod_1seLambda <- ggplot(pred_glm1_1se_full) + 
  geom_point(aes(x = x, y = jitter(missClass2)), alpha = .1) + 
  geom_hline(aes(yintercept = 0), lty = 2, col = "red") + 
  geom_smooth(aes(x = x, y = missClass2)) + 
  xlab("Longitude") + 
  ylab("misclassifications") +
  ggtitle(paste0("from ", name_secondBestMod))

library(patchwork)
(yearResidMod_bestLambda + yearResidMod_1seLambda) / 
(  latResidMod_bestLambda + latResidMod_1seLambda) /
(  longResidMod_bestLambda + longResidMod_1seLambda)
}

Quantile plots - comparing “binary” observations across the full dataset to continuous model-predicted probabilities

Binning predictor variables into “Quantiles”and looking at the mean predicted probability for each quantile

response_vars <- c("TotalTreeCover_binom", "TotalTreeCover_binom_pred")
# get deciles for best lambda model 
if (length(prednames_fig) == 0) {
  print("The best lambda model only contains one predictor (an intercept), so decile plots aren't possible to generate")
} else {
  pred_glm1_deciles <- predvars2deciles(pred_glm1_full,
                                      response_vars = response_vars,
                                        pred_vars = prednames_fig, 
                                       cut_points = seq(0, 1, 0.01))
}
# get deciles for 1 SE lambda model 
if ( name_secondBestMod == "Intercept_Only") {
  print("The next best lambda model only contains one predictor (an intercept)")} else {
  pred_glm1_deciles_1se <- predvars2deciles(pred_glm1_1se_full,
                                      response_vars = response_vars,
                                        pred_vars = prednames_secondBestMod, 
                                       cut_points = seq(0, 1, 0.01))
  }

Below are quantile plots for the best lambda model (note that the predictor variables are scaled)

if (length(prednames_fig) == 0) {
  print("The model only contains one predictor (an intercept), so decile plots aren't possible to generate")
} else {

# publication quality version
g3 <- decile_dotplot_pq(df = pred_glm1_deciles, response = c("TotalTreeCover_binom", paste0("TotalTreeCover_binom", "_pred")), IQR = FALSE,
                        CI = FALSE
                        ) + ggtitle("Decile Plot")

g4 <- add_dotplot_inset(g3, df = pred_glm1_deciles, response = c("TotalTreeCover_binom", paste0("TotalTreeCover_binom", "_pred")), dfRaw = pred_glm1_full, add_smooth = TRUE, deciles = FALSE)

  
if(save_figs) {
  # png(paste0("../../../Figures/CoverDatFigures/ figures/quantile_plots/quantile_plot_", response,  "_",ecoregion,".png"), 
  #    units = "in", res = 600, width = 5.5, height = 3.5 )
  #   print(g4)
  # dev.off()
}

g4
}

Below are quantile plots from the second best lambda model ()

if ( name_secondBestMod == "Intercept_Only") {
  print("The next best lambda model only contains one predictor (an intercept)")
  } else {

# publication quality version
g3 <- decile_dotplot_pq(pred_glm1_deciles_1se, response = c("TotalTreeCover_binom", paste0("TotalTreeCover_binom", "_pred")), IQR = FALSE) + ggtitle("Decile Plot")

g4 <- add_dotplot_inset(g3, df = pred_glm1_deciles_1se, response = c("TotalTreeCover_binom", paste0("TotalTreeCover_binom", "_pred")), dfRaw = pred_glm1_1se_full, add_smooth = TRUE, deciles = FALSE)

  
if(save_figs) {
  # png(paste0("figures/quantile_plots/quantile_plot_", response,  "_",ecoregion,".png"), 
  #    units = "in", res = 600, width = 5.5, height = 3.5 )
  #   print(g4)
  # dev.off()
}

g4
}

Filtered Quantiles - comparing “binary” observations in the testing dataset to continuous model-predicted probabilities

For the best lambda model

Filtered quantile plots of data. These plots show each vegetation variable, but only based on data that falls into the upper and lower 20th percentiles of each predictor variable.

if (length(prednames_fig) == 0) {
  print("The model only contains one predictor (an intercept), so decile plots aren't possible to generate")
} else {
pred_glm1_deciles_filt <- predvars2deciles( pred_glm1_full, 
                         response_vars = c("TotalTreeCover_binom", paste0("TotalTreeCover_binom", "_pred")),
                         pred_vars = prednames_fig,
                         filter_var = TRUE,
                         filter_vars = prednames_fig,
                         cut_points = seq(0, 1, 0.01)) 
g <- decile_dotplot_filtered_pq(df = pred_glm1_deciles_filt, response = "TotalTreeCover_binom", 
                                xvars = prednames_fig)

if(save_figs) {
# jpeg(paste0("figures/quantile_plots/quantile_plot_filtered_mid_v1", , ".jpeg"),
#      units = "in", res = 600, width = 5.5, height = 6 )
#   g 
# dev.off()
}
g
}

Filtered quantile figure with middle 2 deciles also shown

if ( name_secondBestMod == "Intercept_Only") {
  print("The next best lambda model only contains one predictor (an intercept)")
} else {
pred_glm1_deciles_filt_mid <- predvars2deciles(pred_glm1_full, 
                         response_vars = c("TotalTreeCover_binom", paste0("TotalTreeCover_binom", "_pred")),
                         pred_vars = prednames_fig,
                         filter_vars = prednames_fig,
                         filter_var = TRUE,
                         add_mid = TRUE,
                         cut_points = seq(0, 1, 0.01))

g <- decile_dotplot_filtered_pq(df = pred_glm1_deciles_filt_mid, response = "TotalTreeCover_binom", 
                                xvars = prednames_fig)

if(save_figs) {
# jpeg(paste0("figures/quantile_plots/quantile_plot_filtered_mid_v1", , ".jpeg"),
#      units = "in", res = 600, width = 5.5, height = 6)
#   g 
# dev.off()
}
g
}

For the second best lambda model ()

Filtered ‘Quantile’ plots of data. These plots show each vegetation variable, but only based on data that falls into the upper and lower 20th percentiles of each predictor variable.

if (length(prednames_secondBestMod) == 0) {
  print("The model only contains one predictor (an intercept), so decile plots aren't possible to generate")
} else {
  
pred_glm1_deciles_filt <- predvars2deciles( pred_glm1_1se_full, 
                         response_vars = c("TotalTreeCover_binom", paste0("TotalTreeCover_binom", "_pred")),
                         pred_vars = prednames_secondBestMod,
                         filter_var = TRUE,
                         filter_vars = prednames_secondBestMod,
                         cut_points = seq(0, 1, 0.01)) 
g <- decile_dotplot_filtered_pq(df = pred_glm1_deciles_filt, response = "TotalTreeCover_binom", 
                                xvars = prednames_fig)

if(save_figs) {
# jpeg(paste0("figures/quantile_plots/quantile_plot_filtered_mid_v1", , ".jpeg"),
#      units = "in", res = 600, width = 5.5, height = 6 )
#   g 
# dev.off()
}
g
}

Filtered quantile figure with middle 2 deciles also shown

if (length(prednames_secondBestMod) == 0) {
  print("The model only contains one predictor (an intercept), so decile plots aren't possible to generate")
} else {
pred_glm1_deciles_filt_mid <- predvars2deciles(pred_glm1_1se_full, 
                         response_vars = c("TotalTreeCover_binom", paste0("TotalTreeCover_binom", "_pred")),
                         pred_vars = prednames_secondBestMod,
                         filter_vars = prednames_secondBestMod,
                         filter_var = TRUE,
                         add_mid = TRUE,
                         cut_points = seq(0, 1, 0.01))

g <- decile_dotplot_filtered_pq(df = pred_glm1_deciles_filt_mid, response = "TotalTreeCover_binom", 
                                xvars = prednames_fig)


if(save_figs) {
# jpeg(paste0("figures/quantile_plots/quantile_plot_filtered_mid_v1", , ".jpeg"),
#      units = "in", res = 600, width = 5.5, height = 6 )
#   g 
# dev.off()
}
g
}

Quantile plots - comparing “binary” testing data to “binary” model-predictions (i.e. converting the continuous model predictions to discrete values (1 or 0) based on the previously-identified optimal threshold)

response_vars <- c("TotalTreeCover_binom", "TotalTreeCover_binom_pred_binary")
# get deciles for best lambda model 
if (length(prednames_fig) == 0) {
  print("The best lambda model only contains one predictor (an intercept), so decile plots aren't possible to generate")
} else {
  pred_glm1_deciles <- predvars2deciles(pred_glm1_full,
                                      response_vars = response_vars,
                                        pred_vars = prednames_fig, 
                                       cut_points = seq(0, 1, 0.01))
}
# get deciles for 1 SE lambda model 
if ( name_secondBestMod == "Intercept_Only") {
  print("The next best lambda model only contains one predictor (an intercept)")} else {
  pred_glm1_deciles_1se <- predvars2deciles(pred_glm1_1se_full,
                                      response_vars = response_vars,
                                        pred_vars = prednames_secondBestMod, 
                                       cut_points = seq(0, 1, 0.01))
  }

Below are quantile plots for the best lambda model (note that the predictor variables are scaled)

if (length(prednames_fig) == 0) {
  print("The model only contains one predictor (an intercept), so decile plots aren't possible to generate")
} else {
# ####  code to generate plots analagous to "decile plots" by hand, do double check that they're suitable for use w/ binary predictions 
#   pred_glm1 %>% 
#     #slice_sample(n = 10000) %>% 
#     pivot_longer(cols = all_of(prednames_fig)) %>% 
#     select(Year, x, y, TotalTreeCover_binom, TotalTreeCover_binom_pred_binary, name, value) %>% 
#     ggplot() + 
#     facet_wrap(~name, scales = "free") + 
#     geom_point(aes(x = value, y = jitter(TotalTreeCover_binom)), alpha = .5) + 
#     geom_point(aes(x = value, y = jitter(TotalTreeCover_binom_pred_binary)), col = "blue", alpha = .5) + 
#     geom_smooth(aes(x = value, y = TotalTreeCover_binom), col = "black") + 
#     geom_smooth(aes(x = value, y = TotalTreeCover_binom_pred_binary), col = "blue") 
#                  
  
  
  #####
# publication quality version
g3 <- decile_dotplot_pq(df = pred_glm1_deciles, response = c("TotalTreeCover_binom", paste0("TotalTreeCover_binom", "_pred_binary")), IQR = FALSE,
                        CI = FALSE
                        ) + ggtitle("Decile Plot")

g4 <- add_dotplot_inset(g3, df = pred_glm1_deciles, response = c("TotalTreeCover_binom", paste0("TotalTreeCover_binom", "_pred_binary")), dfRaw = pred_glm1_full, add_smooth = TRUE, deciles = FALSE)

  
if(save_figs) {
  # png(paste0("../../../Figures/CoverDatFigures/ figures/quantile_plots/quantile_plot_", response,  "_",ecoregion,".png"), 
  #    units = "in", res = 600, width = 5.5, height = 3.5 )
  #   print(g4)
  # dev.off()
}

g4
}

Below are quantile plots from the second best lambda model (not that the predictor variables are scaled)

if ( name_secondBestMod == "Intercept_Only") {
  print("The next best lambda model only contains one predictor (an intercept)")
  } else {

# publication quality version
g3 <- decile_dotplot_pq(pred_glm1_deciles_1se, response = c("TotalTreeCover_binom", paste0("TotalTreeCover_binom", "_pred_binary")), IQR = FALSE) + ggtitle("Decile Plot")

g4 <- add_dotplot_inset(g3, df = pred_glm1_deciles_1se, response = c("TotalTreeCover_binom", paste0("TotalTreeCover_binom", "_pred_binary")), dfRaw = pred_glm1_1se_full, add_smooth = TRUE, deciles = FALSE)

  
if(save_figs) {
  # png(paste0("figures/quantile_plots/quantile_plot_", response,  "_",ecoregion,".png"), 
  #    units = "in", res = 600, width = 5.5, height = 3.5 )
  #   print(g4)
  # dev.off()
}

g4
}

Show model RMSE w/in each quantile

# get deciles for best lambda model 
if (length(prednames_fig) == 0) {
  print("The best lambda model only contains one predictor (an intercept), so decile plots aren't possible to generate")
} else {
  pred_glm1_deciles %>% 
    ggplot(aes(x = mean_value, y = RMSE)) +
    facet_wrap(~name, scales = "free_x") +
    geom_point(alpha = .2, size = .5) + 
    geom_smooth(lwd = .5) + 
    xlab("Scaled predictor value") + 
    ggtitle("RMSE by decile for bestLambda model")
}

# get deciles for 1 SE lambda model 
if (length(prednames_secondBestMod) == 0) {
  print("The 1SE (or 1/2 SE) lambda model only contains one predictor (an intercept), so decile plots aren't possible to generate")
} else {
  pred_glm1_deciles_1se %>% 
    ggplot(aes(x = mean_value, y = RMSE)) +
    facet_wrap(~name, scales = "free_x") +
    geom_point(alpha = .2, size = .5) + 
    geom_smooth(lwd = .5) + 
    xlab("Scaled predictor value") + 
    ggtitle(paste0("RMSE by decile for ", name_secondBestMod, "model"))
}

Equations for final models

# get the parameters that were used to scale the data
scaleParams <- modDat_1_s_temp %>% 
  filter(Year == 2016) %>% 
  dplyr::select(tmin_s:AWHC_s) %>% 
  reframe(across(all_of(names(.)), attributes)) 

# function for printing model statement
## function to get model statements
getModelStatement <- function(coefficientTable, # name of the d.f that has model coefficients
                  modelName, # name of the column in the coefficient table that has the parameters of interest
                  responseVar # name of the response variable
                  ) {
  ##
  # coefficientTable <- grassShrub_totalHerb_trimAnoms
  # modelName <- "coefficientValue_bestLambda"
  # responseVar <- "TotalHerbaceousCover"
  ##
  temp <- coefficientTable[,c("coefficientName", modelName)] %>% 
    drop_na()
  rownames(temp) <- temp$coefficientName
  temp[,modelName] <- round(temp[,modelName], 8)
  
  # print out coefficients w/ coefficient names
tempNames <- paste0(
  apply(temp, MARGIN = 1, FUN = function(x) {
    if (x["coefficientName"] == "(Intercept)") {
      paste0(x[modelName])
    } else {  
      paste0(x[modelName], "*", x["coefficientName"])
    }
    }
  ),
  collapse = " + "
)

# print the unscaled model statement
  unscaledModelName <- paste0(responseVar, "~ exp(", tempNames, ") - 2")
  
  # now add in the scale parameters
tempNames <- str_replace_all(tempNames, pattern = "annWetDegDays_anom", 
                         replacement = paste0("((annWetDegDays_anom - ", 
                                              round(scaleParams$annWetDegDays_anom_s$`scaled:center`,8), ") / ", 
                                              round(scaleParams$annWetDegDays_anom_s$`scaled:scale`,8), ")"))

tempNames <- str_replace_all(tempNames, pattern = "prcpTempCorr_anom", 
                         replacement = paste0("((prcpTempCorr_anom - ", 
                                              round(scaleParams$prcpTempCorr_anom_s$`scaled:center`,8), ") / ", 
                                              round(scaleParams$prcpTempCorr_anom_s$`scaled:scale`,8), ")"))


tempNames <- str_replace_all(tempNames, pattern = "prcp_seasonality_anom", 
                         replacement = paste0("((prcp_seasonality_anom - ", 
                                              round(scaleParams$prcp_seasonality_anom_s$`scaled:center`,8), ") / ", 
                                              round(scaleParams$prcp_seasonality_anom_s$`scaled:scale`,8), ") "))

tempNames <- str_replace_all(tempNames, pattern = "annWatDef_anom", 
                         replacement = paste0("((annWatDef_anom - ", 
                                              round(scaleParams$annWatDef_anom_s$`scaled:center`,8), ") / ", 
                                              round(scaleParams$annWatDef_anom_s$`scaled:scale`,8), ") "))

tempNames <- str_replace_all(tempNames, pattern = "isothermality_anom", 
                         replacement = paste0("((isothermality_anom - ", 
                                              round(scaleParams$isothermality_anom_s$`scaled:center`,8), ") / ", 
                                              round(scaleParams$isothermality_anom_s$`scaled:scale`,8), ") "))

tempNames <- str_replace_all(tempNames, pattern = "prcp_anom", 
                         replacement = paste0("((prcp_anom - ", 
                                              round(scaleParams$prcp_anom_s$`scaled:center`,8), ") / ", 
                                              round(scaleParams$prcp_anom_s$`scaled:scale`,8), ") "))

tempNames <- str_replace_all(tempNames, pattern = "prcp ", 
                         replacement = paste0("((prcp - ", 
                                              round(scaleParams$prcp_s$`scaled:center`,8), ") / ", 
                                              round(scaleParams$prcp_s$`scaled:scale`,8), ") "))

tempNames <- str_replace_all(tempNames, pattern = "prcp\\^", 
                         replacement = paste0("((prcp - ", 
                                              round(scaleParams$prcp_s$`scaled:center`,8), ") / ", 
                                              round(scaleParams$prcp_s$`scaled:scale`,8), ")^"))

tempNames <- str_replace_all(tempNames, pattern = "prcp:", 
                         replacement = paste0("((prcp - ", 
                                              round(scaleParams$prcp_s$`scaled:center`,8), ") / ", 
                                              round(scaleParams$prcp_s$`scaled:scale`,8), "):"))

tempNames <- str_replace_all(tempNames, pattern = "prcpTempCorr ", 
                         replacement = paste0("((prcpTempCorr - ", 
                                              round(scaleParams$prcpTempCorr_s$`scaled:center`,8), ") / ", 
                                              round(scaleParams$prcpTempCorr_s$`scaled:scale`,8), ") "))

tempNames <- str_replace_all(tempNames, pattern = "prcpTempCorr\\^", 
                         replacement = paste0("((prcpTempCorr - ", 
                                              round(scaleParams$prcpTempCorr_s$`scaled:center`,8), ") / ", 
                                              round(scaleParams$prcpTempCorr_s$`scaled:scale`,8), ")^"))

tempNames <- str_replace_all(tempNames, pattern = "prcpTempCorr:", 
                         replacement = paste0("((prcpTempCorr - ", 
                                              round(scaleParams$prcpTempCorr_s$`scaled:center`,8), ") / ", 
                                              round(scaleParams$prcpTempCorr_s$`scaled:scale`,8), "):"))

tempNames <- str_replace_all(tempNames, pattern = "prcpTempCorr\\)", 
                         replacement = paste0("((prcpTempCorr - ", 
                                              round(scaleParams$prcpTempCorr_s$`scaled:center`,8), ") / ", 
                                              round(scaleParams$prcpTempCorr_s$`scaled:scale`,8), "))"))

tempNames <- str_replace_all(tempNames, pattern = "prcpTempCorr$", 
                         replacement = paste0("((prcpTempCorr - ", 
                                              round(scaleParams$prcpTempCorr_s$`scaled:center`,8), ") / ", 
                                              round(scaleParams$prcpTempCorr_s$`scaled:scale`,8), ")"))

tempNames <- str_replace_all(tempNames, pattern = "isothermality ", 
                         replacement = paste0("((isothermality - ", 
                                              round(scaleParams$isothermality_s$`scaled:center`,8), ") / ", 
                                              round(scaleParams$isothermality_s$`scaled:scale`,8), ") "))

tempNames <- str_replace_all(tempNames, pattern = "isothermality\\^", 
                         replacement = paste0("((isothermality - ", 
                                              round(scaleParams$isothermality_s$`scaled:center`,8), ") / ", 
                                              round(scaleParams$isothermality_s$`scaled:scale`,8), ")^"))

tempNames <- str_replace_all(tempNames, pattern = "isothermality:", 
                         replacement = paste0("((isothermality - ", 
                                              round(scaleParams$isothermality_s$`scaled:center`,8), ") / ", 
                                              round(scaleParams$isothermality_s$`scaled:scale`,8), "):"))

tempNames <- str_replace_all(tempNames, pattern = "sand", 
                         replacement = paste0("((sand - ", 
                                              round(scaleParams$sand_s$`scaled:center`,8), ") / ", 
                                              round(scaleParams$sand_s$`scaled:scale`,8), ")"))

tempNames <- str_replace_all(tempNames, pattern = "coarse", 
                         replacement = paste0("((coarse - ", 
                                              round(scaleParams$coarse_s$`scaled:center`,8), ") / ", 
                                              round(scaleParams$coarse_s$`scaled:scale`,8), ")"))

tempNames <- str_replace_all(tempNames, pattern = "AWHC", 
                         replacement = paste0("((AWHC - ", 
                                              round(scaleParams$AWHC_s$`scaled:center`,8), ") / ", 
                                              round(scaleParams$AWHC_s$`scaled:scale`,8), ")"))

tempNames <- str_replace_all(tempNames, pattern = "carbon", 
                         replacement = paste0("((carbon - ", 
                                              round(scaleParams$carbon_s$`scaled:center`,8), ") / ", 
                                              round(scaleParams$carbon_s$`scaled:scale`,8), ")"))

tempNames <- str_replace_all(tempNames, pattern = "clay", 
                         replacement = paste0("((clay - ", 
                                              round(scaleParams$clay_s$`scaled:center`,8), ") / ", 
                                              round(scaleParams$clay_s$`scaled:scale`,8), ")"))

tempNames <- str_replace_all(tempNames, pattern = "annWatDef ", 
                         replacement = paste0("((annWatDef - ", 
                                              round(scaleParams$annWatDef_s$`scaled:center`,8), ") / ", 
                                              round(scaleParams$annWatDef_s$`scaled:scale`,8), ") "))

tempNames <- str_replace_all(tempNames, pattern = "annWatDef:", 
                         replacement = paste0("((annWatDef - ", 
                                              round(scaleParams$annWatDef_s$`scaled:center`,8), ") / ", 
                                              round(scaleParams$annWatDef_s$`scaled:scale`,8), "):"))

tempNames <- str_replace_all(tempNames, pattern = "prcp_seasonality ", 
                         replacement = paste0("((prcp_seasonality - ", 
                                              round(scaleParams$prcp_seasonality_s$`scaled:center`,8), ") / ", 
                                              round(scaleParams$prcp_seasonality_s$`scaled:scale`,8), ") "))

tempNames <- str_replace_all(tempNames, pattern = "prcp_seasonality:", 
                         replacement = paste0("((prcp_seasonality - ", 
                                              round(scaleParams$prcp_seasonality_s$`scaled:center`,8), ") / ", 
                                              round(scaleParams$prcp_seasonality_s$`scaled:scale`,8), "):"))

tempNames <- str_replace_all(tempNames, pattern = "prcp_seasonality\\^", 
                         replacement = paste0("((prcp_seasonality - ", 
                                              round(scaleParams$prcp_seasonality_s$`scaled:center`,8), ") / ", 
                                              round(scaleParams$prcp_seasonality_s$`scaled:scale`,8), ")^"))

tempNames <- str_replace_all(tempNames, pattern = "tmean ", 
                         replacement = paste0("((tmean - ", 
                                              round(scaleParams$tmean_s$`scaled:center`,8), ") / ", 
                                              round(scaleParams$tmean_s$`scaled:scale`,8), ") "))

tempNames <- str_replace_all(tempNames, pattern = "tmean:", 
                         replacement = paste0("((tmean - ", 
                                              round(scaleParams$tmean_s$`scaled:center`,8), ") / ", 
                                              round(scaleParams$tmean_s$`scaled:scale`,8), "):"))

tempNames <- str_replace_all(tempNames, pattern = "tmean$", 
                         replacement = paste0("((tmean - ", 
                                              round(scaleParams$tmean_s$`scaled:center`,8), ") / ", 
                                              round(scaleParams$tmean_s$`scaled:scale`,8), ")"))

tempNames <- str_replace_all(tempNames, pattern = "tmean\\^", 
                         replacement = paste0("((tmean - ", 
                                              round(scaleParams$tmean_s$`scaled:center`,8), ") / ", 
                                              round(scaleParams$tmean_s$`scaled:scale`,8), ")^"))

tempNames <- str_replace_all(tempNames, pattern = "annWetDegDays ", 
                         replacement = paste0("((annWetDegDays - ", 
                                              round(scaleParams$annWetDegDays_s$`scaled:center`,8), ") / ", 
                                              round(scaleParams$annWetDegDays_s$`scaled:scale`,8), ") "))

tempNames <- str_replace_all(tempNames, pattern = "annWetDegDays:", 
                         replacement = paste0("((annWetDegDays - ", 
                                              round(scaleParams$annWetDegDays_s$`scaled:center`,8), ") / ", 
                                              round(scaleParams$annWetDegDays_s$`scaled:scale`,8), "):"))

tempNames <- str_replace_all(tempNames, pattern = "prcp_dry ", 
                         replacement = paste0("((prcp_dry - ", 
                                              round(scaleParams$prcp_dry_s$`scaled:center`,8), ") / ", 
                                              round(scaleParams$prcp_dry_s$`scaled:scale`,8), ") "))

tempNames <- str_replace_all(tempNames, pattern = "prcp_dry:", 
                         replacement = paste0("((prcp_dry - ", 
                                              round(scaleParams$prcp_dry_s$`scaled:center`,8), ") / ", 
                                              round(scaleParams$prcp_dry_s$`scaled:scale`,8), "):"))

tempNames <- str_replace_all(tempNames, pattern = "annWatDef_95", 
                         replacement = paste0("((annWatDef_95 - ", 
                                              round(scaleParams$annWatDef_95_s$`scaled:center`,8), ") / ", 
                                              round(scaleParams$annWatDef_95_s$`scaled:scale`,8), ")"))


## print scaled model statement

scaledModelName <- paste0(responseVar, "~ exp(", tempNames, ")")
  
return(list("scaledInputVars_ModelStatement" = unscaledModelName, 
            "unscaledInputVars_scaledModelStatement" = scaledModelName))
}


## bestLambda model equations
bestLambdaModStatement <- getModelStatement(coefficientTable = coefs, 
                  modelName = "coefficientValue_bestLambda", 
                  responseVar = "P(Tree)")
## second-best lambda model equations
secondBestLambdaModStatement <- getModelStatement(coefficientTable = coefs, 
                  modelName = ifelse(name_secondBestMod == "1/2 SE Model", 
                                      yes = "coefficientValue_halfseLambda", 
                                     no = "coefficientValue_1seLambda"), 
                  responseVar = "P(Tree)")

The equation for the bestLambda model if the inputs are scaled is:

print(bestLambdaModStatement$scaledInputVars_ModelStatement)

## [1] "P(Tree)~ exp(-0.67478165 +  1.71345065*prcp + -0.01633932*prcp_seasonality + -0.91285243*prcpTempCorr +  0.53377439*annWetDegDays + -0.60523936*annWatDef_95 +  0.20578879*coarse + -0.61568228*AWHC + -0.31818631*I(tmean^2) +  0.20104126*I(prcp_seasonality^2) + -0.89055646*I(prcpTempCorr^2) +  0.14226917*I(isothermality^2) + -0.11810211*I(clay^2) +  0.11278028*I(AWHC^2) +  0.91656456*annWetDegDays:annWatDef_95 + -0.29650844*prcp_dry:isothermality + -0.02061048*prcpTempCorr:isothermality + -0.28504255*isothermality:tmean +  0.50549093*prcpTempCorr:prcp_dry + -0.25285633*prcpTempCorr:tmean + -0.16290284*AWHC:clay +  0.09163249*coarse:clay) - 2"

The equation for the bestLambda model if the inputs are NOT scaled is:

print(bestLambdaModStatement$unscaledInputVars_scaledModelStatement)

## [1] "P(Tree)~ exp(-0.67478165 +  1.71345065*((prcp - 483.34337211) / 321.52170566) + -0.01633932*((prcp_seasonality - 0.97338094) / 0.23365057) + -0.91285243*((prcpTempCorr - 0.01681097) / 0.39882063) +  0.53377439*((annWetDegDays - 1808.61043539) / 1083.25298131) + -0.60523936*((annWatDef_95 - 164.68611646) / 104.14892564) +  0.20578879*((coarse - 9.66120017) / 10.16883531) + -0.61568228*((AWHC - 14.61190409) / 5.65765542) + -0.31818631*I(((tmean - 11.0291275) / 4.89048541)^2) +  0.20104126*I(((prcp_seasonality - 0.97338094) / 0.23365057)^2) + -0.89055646*I(((prcpTempCorr - 0.01681097) / 0.39882063)^2) +  0.14226917*I(((isothermality - 37.76731082) / 5.2256935)^2) + -0.11810211*I(((clay - 19.59171509) / 8.51944876)^2) +  0.11278028*I(((AWHC - 14.61190409) / 5.65765542)^2) +  0.91656456*((annWetDegDays - 1808.61043539) / 1083.25298131):((annWatDef_95 - 164.68611646) / 104.14892564) + -0.29650844*((prcp_dry - 3.18622575) / 5.36400552):((isothermality - 37.76731082) / 5.2256935) + -0.02061048*((prcpTempCorr - 0.01681097) / 0.39882063):((isothermality - 37.76731082) / 5.2256935) + -0.28504255*((isothermality - 37.76731082) / 5.2256935):((tmean - 11.0291275) / 4.89048541) +  0.50549093*((prcpTempCorr - 0.01681097) / 0.39882063):((prcp_dry - 3.18622575) / 5.36400552) + -0.25285633*((prcpTempCorr - 0.01681097) / 0.39882063):((tmean - 11.0291275) / 4.89048541) + -0.16290284*((AWHC - 14.61190409) / 5.65765542):((clay - 19.59171509) / 8.51944876) +  0.09163249*((coarse - 9.66120017) / 10.16883531):((clay - 19.59171509) / 8.51944876))"

The equation for the second-bestLambda model if the inputs are scaled is:

print(secondBestLambdaModStatement$scaledInputVars_ModelStatement)

## [1] "P(Tree)~ exp(-0.8616112 +  1.9694935*prcp + -0.3086721*prcp_seasonality + -0.5967287*prcpTempCorr + -0.7655963*AWHC + -0.6416890*I(prcpTempCorr^2) + -0.1661580*I(clay^2) + -0.4376182*prcp_dry:isothermality + -0.2506869*AWHC:clay) - 2"

The equation for the second-bestLambda model if the inputs are NOT scaled is:

print(secondBestLambdaModStatement$unscaledInputVars_scaledModelStatement)

## [1] "P(Tree)~ exp(-0.8616112 +  1.9694935*((prcp - 483.34337211) / 321.52170566) + -0.3086721*((prcp_seasonality - 0.97338094) / 0.23365057) + -0.5967287*((prcpTempCorr - 0.01681097) / 0.39882063) + -0.7655963*((AWHC - 14.61190409) / 5.65765542) + -0.6416890*I(((prcpTempCorr - 0.01681097) / 0.39882063)^2) + -0.1661580*I(((clay - 19.59171509) / 8.51944876)^2) + -0.4376182*((prcp_dry - 3.18622575) / 5.36400552):((isothermality - 37.76731082) / 5.2256935) + -0.2506869*((AWHC - 14.61190409) / 5.65765542):((clay - 19.59171509) / 8.51944876))"

Now, use the model to predict if a location is or is not trees, for all observations in the cover dataset (which we will use in the subsequent step of the cover-modelign process).

We use the ‘modDat_1_s_temp’ data.frame, which has all of the cover data, even for locations without observed tree cover, but has the climate and soils data that have been scaled in that same was as the data we used to fit the yes/no tree model

# prep data
modDat_1_s_temp$rowID <- 1:nrow(modDat_1_s_temp)
predData <- modDat_1_s_temp %>% 
  select(rowID, Year, x, y, paste0(prednames, "_s")) %>% 
  rename_with(~str_remove(.x, "_s$"), 
              any_of(paste0(names(prednames), "_s")))
# for bestLambda model
predData$treeProb_bestLambda <- predict.glm(object = fit_glm_bestLambda, newdata = predData, type = "response")
# for scond-bestLambda model
predData$treeProb_secondBestLambda <- predict.glm(object = mod_secondBest, newdata = predData, type = "response")

# make continuous predictions binary according to the identified best threshold for each model 
predData <- predData %>% 
  mutate(treeProb_bestLambda_binary = treeProb_bestLambda,
    treeProb_bestLambda_binary = replace(treeProb_bestLambda_binary, treeProb_bestLambda_binary > best_threshold_bestLambda, 1),
         treeProb_bestLambda_binary = replace(treeProb_bestLambda_binary, treeProb_bestLambda_binary <= best_threshold_bestLambda, 0)) %>% 
  mutate(treeProb_secondBestLambda_binary = treeProb_secondBestLambda,
    treeProb_secondBestLambda_binary = replace(treeProb_secondBestLambda_binary, treeProb_secondBestLambda_binary > best_threshold_secondBest, 1),
         treeProb_secondBestLambda_binary = replace(treeProb_secondBestLambda_binary, treeProb_secondBestLambda_binary <= best_threshold_secondBest, 0))
  
# add predictions back to the original data frame and save 
modDat_treePreds <- modDat_1_s_temp %>% 
  left_join(predData %>% select(-c(tmean:AWHC)), by = c("rowID", "Year", "x", "y")) %>% 
  select(-c(tmin_s:AWHC_s))

saveRDS(modDat_treePreds,"../../../Data_processed/CoverData/CoverModelData_withTreeNoTreePreds.rds")